LMFDB - Embedded newform 819.2.fy.a.743.82

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [819,2,Mod(50,819)]

mf = mfinit([N,k,chi],0)

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(819, base_ring=CyclotomicField(12))

chi = DirichletCharacter(H, H._module([10, 0, 7]))

N = Newforms(chi, 2, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("819.50");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 819 = 3^{2} \cdot 7 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	819.fy (of order $12$, degree $4$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$6.53974792554$
Analytic rank:	$0$
Dimension:	$336$
Relative dimension:	$84$ over $\Q(\zeta_{12})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			743.82
Character	$\chi$	$=$	819.743
Dual form			819.2.fy.a.722.82

$q$-expansion

comment: q-expansion

sage: f.q_expansion() # note that sage often uses an isomorphic number field

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(2.58695 - 0.693172i) q^{2} +(0.748276 - 1.56208i) q^{3} +(4.47979 - 2.58641i) q^{4} +(-1.50795 + 0.404053i) q^{5} +(0.852967 - 4.55970i) q^{6} +(-0.707107 - 0.707107i) q^{7} +(6.00863 - 6.00863i) q^{8} +(-1.88017 - 2.33773i) q^{9} +O(q^{10})$	\(q+(2.58695 - 0.693172i) q^{2} +(0.748276 - 1.56208i) q^{3} +(4.47979 - 2.58641i) q^{4} +(-1.50795 + 0.404053i) q^{5} +(0.852967 - 4.55970i) q^{6} +(-0.707107 - 0.707107i) q^{7} +(6.00863 - 6.00863i) q^{8} +(-1.88017 - 2.33773i) q^{9} +(-3.62091 + 2.09054i) q^{10} +(0.0866523 + 0.323391i) q^{11} +(-0.688050 - 8.93313i) q^{12} +(2.67187 + 2.42098i) q^{13} +(-2.31940 - 1.33911i) q^{14} +(-0.497198 + 2.65787i) q^{15} +(6.20621 - 10.7495i) q^{16} +(-2.33857 + 4.05053i) q^{17} +(-6.48435 - 4.74432i) q^{18} +(-0.231444 - 0.863760i) q^{19} +(-5.71025 + 5.71025i) q^{20} +(-1.63367 + 0.575444i) q^{21} +(0.448331 + 0.776532i) q^{22} +1.01562 q^{23} +(-4.88983 - 13.8820i) q^{24} +(-2.21948 + 1.28142i) q^{25} +(8.59015 + 4.41089i) q^{26} +(-5.05859 + 1.18770i) q^{27} +(-4.99656 - 1.33882i) q^{28} +(8.28025 + 4.78060i) q^{29} +(0.556135 + 7.22044i) q^{30} +(0.559255 + 2.08717i) q^{31} +(4.20532 - 15.6945i) q^{32} +(0.570001 + 0.106628i) q^{33} +(-3.24207 + 12.0996i) q^{34} +(1.35199 + 0.780571i) q^{35} +(-14.4691 - 5.60965i) q^{36} +(2.10164 - 7.84344i) q^{37} +(-1.19747 - 2.07408i) q^{38} +(5.78104 - 2.36211i) q^{39} +(-6.63289 + 11.4885i) q^{40} +(-2.64521 - 2.64521i) q^{41} +(-3.82734 + 2.62106i) q^{42} -4.57750i q^{43} +(1.22460 + 1.22460i) q^{44} +(3.77976 + 2.76548i) q^{45} +(2.62737 - 0.704002i) q^{46} +(1.77688 + 0.476115i) q^{47} +(-12.1475 - 17.7381i) q^{48} +1.00000i q^{49} +(-4.85345 + 4.85345i) q^{50} +(4.57734 + 6.68394i) q^{51} +(18.2310 + 3.93492i) q^{52} +6.95452i q^{53} +(-12.2631 + 6.57900i) q^{54} +(-0.261334 - 0.452644i) q^{55} -8.49748 q^{56} +(-1.52244 - 0.284798i) q^{57} +(24.7344 + 6.62756i) q^{58} +(-1.67038 - 0.447578i) q^{59} +(4.64700 + 13.1927i) q^{60} -6.07889 q^{61} +(2.89353 + 5.01175i) q^{62} +(-0.323544 + 2.98250i) q^{63} -18.6911i q^{64} +(-5.00724 - 2.57113i) q^{65} +(1.54848 - 0.119267i) q^{66} +(7.63081 - 7.63081i) q^{67} +24.1940i q^{68} +(0.759967 - 1.58648i) q^{69} +(4.03860 + 1.08214i) q^{70} +(-3.72104 + 0.997051i) q^{71} +(-25.3438 - 2.74931i) q^{72} +(11.8270 + 11.8270i) q^{73} -21.7474i q^{74} +(0.340889 + 4.42585i) q^{75} +(-3.27086 - 3.27086i) q^{76} +(0.167399 - 0.289944i) q^{77} +(13.3179 - 10.1179i) q^{78} +(-3.30393 - 5.72257i) q^{79} +(-5.01528 + 18.7173i) q^{80} +(-1.92994 + 8.79064i) q^{81} +(-8.67662 - 5.00945i) q^{82} +(-3.32038 + 12.3918i) q^{83} +(-5.83015 + 6.80320i) q^{84} +(1.88982 - 7.05289i) q^{85} +(-3.17300 - 11.8418i) q^{86} +(13.6636 - 9.35717i) q^{87} +(2.46379 + 1.42247i) q^{88} +(1.18220 + 0.316770i) q^{89} +(11.6950 + 4.53416i) q^{90} +(-0.177408 - 3.60118i) q^{91} +(4.54979 - 2.62682i) q^{92} +(3.67879 + 0.688178i) q^{93} +4.92675 q^{94} +(0.698010 + 1.20899i) q^{95} +(-21.3692 - 18.3128i) q^{96} +(-8.68421 + 8.68421i) q^{97} +(0.693172 + 2.58695i) q^{98} +(0.593079 - 0.810598i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 336 q - 12 q^{6} + 36 q^{8}+O(q^{10}) $ 336 * q - 12 * q^6 + 36 * q^8	$ 336 q - 12 q^{6} + 36 q^{8} - 12 q^{11} + 4 q^{15} + 168 q^{16} - 4 q^{18} - 4 q^{21} + 8 q^{24} - 96 q^{26} + 24 q^{27} - 120 q^{30} - 72 q^{32} + 36 q^{33} + 72 q^{38} + 8 q^{39} - 48 q^{41} - 76 q^{45} + 24 q^{48} - 24 q^{50} - 36 q^{52} + 72 q^{54} + 32 q^{57} + 36 q^{58} - 72 q^{59} + 4 q^{60} + 36 q^{62} - 8 q^{63} - 72 q^{65} - 20 q^{66} - 48 q^{71} - 176 q^{72} - 60 q^{75} - 124 q^{78} - 12 q^{79} - 96 q^{80} - 20 q^{81} - 156 q^{83} - 12 q^{84} - 108 q^{85} - 24 q^{87} + 60 q^{89} - 72 q^{92} + 20 q^{93} + 96 q^{94} + 88 q^{96} - 96 q^{97} + 108 q^{99}+O(q^{100}) $ 336 * q - 12 * q^6 + 36 * q^8 - 12 * q^11 + 4 * q^15 + 168 * q^16 - 4 * q^18 - 4 * q^21 + 8 * q^24 - 96 * q^26 + 24 * q^27 - 120 * q^30 - 72 * q^32 + 36 * q^33 + 72 * q^38 + 8 * q^39 - 48 * q^41 - 76 * q^45 + 24 * q^48 - 24 * q^50 - 36 * q^52 + 72 * q^54 + 32 * q^57 + 36 * q^58 - 72 * q^59 + 4 * q^60 + 36 * q^62 - 8 * q^63 - 72 * q^65 - 20 * q^66 - 48 * q^71 - 176 * q^72 - 60 * q^75 - 124 * q^78 - 12 * q^79 - 96 * q^80 - 20 * q^81 - 156 * q^83 - 12 * q^84 - 108 * q^85 - 24 * q^87 + 60 * q^89 - 72 * q^92 + 20 * q^93 + 96 * q^94 + 88 * q^96 - 96 * q^97 + 108 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/819\mathbb{Z}\right)^\times$.

$n$	$92$	$379$	$703$
$\chi(n)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{1}{12}\right)$	$1$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$	2.58695	−	0.693172i	1.82925	−	0.490147i	0.831402	−	0.555672i	$-0.187539\pi$
$2$	2.58695	−	0.693172i	1.82925	−	0.490147i	0.997851	+	0.0655250i	$0.0208722\pi$
$3$	0.748276	−	1.56208i	0.432017	−	0.901865i
$3$	0.748276	−	1.56208i	0.432017	−	0.901865i
$4$	4.47979	−	2.58641i	2.23990	−	1.29320i
$5$	−1.50795	+	0.404053i	−0.674375	+	0.180698i	−0.579725	−	0.814812i	$-0.696840\pi$
$5$	−1.50795	+	0.404053i	−0.674375	+	0.180698i	−0.0946502	+	0.995511i	$0.530173\pi$
$6$	0.852967	−	4.55970i	0.348222	−	1.86149i
$7$	−0.707107	−	0.707107i	−0.267261	−	0.267261i
$7$	−0.707107	−	0.707107i	−0.267261	−	0.267261i
$8$	6.00863	−	6.00863i	2.12437	−	2.12437i
$9$	−1.88017	−	2.33773i	−0.626722	−	0.779243i
$10$	−3.62091	+	2.09054i	−1.14503	+	0.661085i
$11$	0.0866523	+	0.323391i	0.0261266	+	0.0975059i	0.977758	−	0.209736i	$-0.0672605\pi$
$11$	0.0866523	+	0.323391i	0.0261266	+	0.0975059i	−0.951631	+	0.307242i	$0.900594\pi$
$12$	−0.688050	−	8.93313i	−0.198623	−	2.57877i
$13$	2.67187	+	2.42098i	0.741043	+	0.671458i
$13$	2.67187	+	2.42098i	0.741043	+	0.671458i
$14$	−2.31940	−	1.33911i	−0.619886	−	0.357891i
$15$	−0.497198	+	2.65787i	−0.128376	+	0.686260i
$16$	6.20621	−	10.7495i	1.55155	−	2.68737i
$17$	−2.33857	+	4.05053i	−0.567187	+	0.982397i	0.429655	+	0.902993i	$0.358635\pi$
$17$	−2.33857	+	4.05053i	−0.567187	+	0.982397i	−0.996843	+	0.0794041i	$0.974698\pi$
$18$	−6.48435	−	4.74432i	−1.52838	−	1.11825i
$19$	−0.231444	−	0.863760i	−0.0530968	−	0.198160i	0.934282	−	0.356534i	$-0.116042\pi$
$19$	−0.231444	−	0.863760i	−0.0530968	−	0.198160i	−0.987379	+	0.158374i	$0.949375\pi$
$20$	−5.71025	+	5.71025i	−1.27685	+	1.27685i
$21$	−1.63367	+	0.575444i	−0.356495	+	0.125572i
$22$	0.448331	+	0.776532i	0.0955844	+	0.165557i
$23$	1.01562			0.211772			0.105886	−	0.994378i	$-0.466232\pi$
$23$	1.01562			0.211772			0.105886	+	0.994378i	$0.466232\pi$
$24$	−4.88983	−	13.8820i	−0.998131	−	2.83366i
$25$	−2.21948	+	1.28142i	−0.443896	+	0.256283i
$26$	8.59015	+	4.41089i	1.68467	+	0.865046i
$27$	−5.05859	+	1.18770i	−0.973527	+	0.228573i
$28$	−4.99656	−	1.33882i	−0.944261	−	0.253014i
$29$	8.28025	+	4.78060i	1.53760	+	0.887736i	0.998978	+	0.0451902i	$0.0143894\pi$
$29$	8.28025	+	4.78060i	1.53760	+	0.887736i	0.538625	+	0.842546i	$0.318944\pi$
$30$	0.556135	+	7.22044i	0.101536	+	1.31827i
$31$	0.559255	+	2.08717i	0.100445	+	0.374867i	0.997789	−	0.0664663i	$-0.0211725\pi$
$31$	0.559255	+	2.08717i	0.100445	+	0.374867i	−0.897343	+	0.441333i	$0.854506\pi$
$32$	4.20532	−	15.6945i	0.743403	−	2.77442i
$33$	0.570001	+	0.106628i	0.0992244	+	0.0185615i
$34$	−3.24207	+	12.0996i	−0.556010	+	2.07506i
$35$	1.35199	+	0.780571i	0.228528	+	0.131941i
$36$	−14.4691	−	5.60965i	−2.41151	−	0.934942i
$37$	2.10164	−	7.84344i	0.345508	−	1.28945i	−0.546510	−	0.837453i	$-0.684044\pi$
$37$	2.10164	−	7.84344i	0.345508	−	1.28945i	0.892018	−	0.452001i	$-0.149290\pi$
$38$	−1.19747	−	2.07408i	−0.194255	−	0.336460i
$39$	5.78104	−	2.36211i	0.925708	−	0.378240i
$40$	−6.63289	+	11.4885i	−1.04875	+	1.81649i
$41$	−2.64521	−	2.64521i	−0.413112	−	0.413112i	0.469709	−	0.882821i	$-0.344359\pi$
$41$	−2.64521	−	2.64521i	−0.413112	−	0.413112i	−0.882821	+	0.469709i	$0.844359\pi$
$42$	−3.82734	+	2.62106i	−0.590571	+	0.404438i
$43$		−	4.57750i		−	0.698063i	−0.937111	−	0.349031i	$-0.886511\pi$
$43$		−	4.57750i		−	0.698063i	0.937111	−	0.349031i	$-0.113489\pi$
$44$	1.22460	+	1.22460i	0.184616	+	0.184616i
$45$	3.77976	+	2.76548i	0.563454	+	0.412254i
$46$	2.62737	−	0.704002i	0.387385	−	0.103800i
$47$	1.77688	+	0.476115i	0.259185	+	0.0694484i	0.386072	−	0.922469i	$-0.373832\pi$
$47$	1.77688	+	0.476115i	0.259185	+	0.0694484i	−0.126887	+	0.991917i	$0.540498\pi$
$48$	−12.1475	−	17.7381i	−1.75335	−	2.56028i
$49$			1.00000i			0.142857i
$50$	−4.85345	+	4.85345i	−0.686381	+	0.686381i
$51$	4.57734	+	6.68394i	0.640955	+	0.935939i
$52$	18.2310	+	3.93492i	2.52819	+	0.545676i
$53$			6.95452i			0.955277i	0.878557	+	0.477638i	$0.158507\pi$
$53$			6.95452i			0.955277i	−0.878557	+	0.477638i	$0.841493\pi$
$54$	−12.2631	+	6.57900i	−1.66879	+	0.895289i
$55$	−0.261334	−	0.452644i	−0.0352383	−	0.0610345i
$56$	−8.49748			−1.13552
$57$	−1.52244	−	0.284798i	−0.201652	−	0.0377224i
$58$	24.7344	+	6.62756i	3.24779	+	0.870242i
$59$	−1.67038	−	0.447578i	−0.217465	−	0.0582696i	0.148441	−	0.988921i	$-0.452574\pi$
$59$	−1.67038	−	0.447578i	−0.217465	−	0.0582696i	−0.365907	+	0.930652i	$0.619241\pi$
$60$	4.64700	+	13.1927i	0.599926	+	1.70317i
$61$	−6.07889			−0.778322			−0.389161	−	0.921170i	$-0.627235\pi$
$61$	−6.07889			−0.778322			−0.389161	+	0.921170i	$0.627235\pi$
$62$	2.89353	+	5.01175i	0.367479	+	0.636493i
$63$	−0.323544	+	2.98250i	−0.0407628	+	0.375760i
$64$		−	18.6911i		−	2.33638i
$65$	−5.00724	−	2.57113i	−0.621072	−	0.318909i
$66$	1.54848	−	0.119267i	0.190604	−	0.0146808i
$67$	7.63081	−	7.63081i	0.932251	−	0.932251i	−0.0655949	−	0.997846i	$-0.520895\pi$
$67$	7.63081	−	7.63081i	0.932251	−	0.932251i	0.997846	+	0.0655949i	$0.0208945\pi$
$68$			24.1940i			2.93396i
$69$	0.759967	−	1.58648i	0.0914893	−	0.190990i
$70$	4.03860	+	1.08214i	0.482706	+	0.129341i
$71$	−3.72104	+	0.997051i	−0.441607	+	0.118328i	−0.472769	−	0.881186i	$-0.656746\pi$
$71$	−3.72104	+	0.997051i	−0.441607	+	0.118328i	0.0311628	+	0.999514i	$0.490079\pi$
$72$	−25.3438	−	2.74931i	−2.98679	−	0.324010i
$73$	11.8270	+	11.8270i	1.38425	+	1.38425i	0.836916	+	0.547332i	$0.184356\pi$
$73$	11.8270	+	11.8270i	1.38425	+	1.38425i	0.547332	+	0.836916i	$0.315644\pi$
$74$		−	21.7474i		−	2.52809i
$75$	0.340889	+	4.42585i	0.0393625	+	0.511053i
$76$	−3.27086	−	3.27086i	−0.375193	−	0.375193i
$77$	0.167399	−	0.289944i	0.0190769	−	0.0330422i
$78$	13.3179	−	10.1179i	1.50796	−	1.14563i
$79$	−3.30393	−	5.72257i	−0.371721	−	0.643839i	0.618110	−	0.786092i	$-0.287899\pi$
$79$	−3.30393	−	5.72257i	−0.371721	−	0.643839i	−0.989830	+	0.142253i	$0.954565\pi$
$80$	−5.01528	+	18.7173i	−0.560725	+	2.09266i
$81$	−1.92994	+	8.79064i	−0.214438	+	0.976738i
$82$	−8.67662	−	5.00945i	−0.958173	−	0.553201i
$83$	−3.32038	+	12.3918i	−0.364459	+	1.36018i	0.503694	+	0.863882i	$0.331974\pi$
$83$	−3.32038	+	12.3918i	−0.364459	+	1.36018i	−0.868153	+	0.496297i	$0.834693\pi$
$84$	−5.83015	+	6.80320i	−0.636121	+	0.742290i
$85$	1.88982	−	7.05289i	0.204979	−	0.764994i
$86$	−3.17300	−	11.8418i	−0.342153	−	1.27693i
$87$	13.6636	−	9.35717i	1.46489	−	1.00319i
$88$	2.46379	+	1.42247i	0.262641	+	0.151636i
$89$	1.18220	+	0.316770i	0.125313	+	0.0335775i	0.320930	−	0.947103i	$-0.396004\pi$
$89$	1.18220	+	0.316770i	0.125313	+	0.0335775i	−0.195617	+	0.980680i	$0.562671\pi$
$90$	11.6950	+	4.53416i	1.23276	+	0.477942i
$91$	−0.177408	−	3.60118i	−0.0185974	−	0.377507i
$92$	4.54979	−	2.62682i	0.474348	−	0.273865i
$93$	3.67879	+	0.688178i	0.381473	+	0.0713607i
$94$	4.92675			0.508155
$95$	0.698010	+	1.20899i	0.0716143	+	0.124040i
$96$	−21.3692	−	18.3128i	−2.18099	−	1.86905i
$97$	−8.68421	+	8.68421i	−0.881748	+	0.881748i	−0.993712	−	0.111965i	$-0.964286\pi$
$97$	−8.68421	+	8.68421i	−0.881748	+	0.881748i	0.111965	+	0.993712i	$0.464286\pi$
$98$	0.693172	+	2.58695i	0.0700210	+	0.261322i
$99$	0.593079	−	0.810598i	0.0596066	−	0.0814681i
$100$	−6.62854	+	11.4810i	−0.662854	+	1.14810i
$101$	3.06298	−	5.30524i	0.304778	−	0.527891i	−0.672434	−	0.740157i	$-0.734751\pi$
$101$	3.06298	−	5.30524i	0.304778	−	0.527891i	0.977212	+	0.212266i	$0.0680844\pi$
$102$	16.4745	+	14.1182i	1.63122	+	1.39791i
$103$	−16.9382	−	9.77929i	−1.66897	−	0.963582i	−0.968193	−	0.250203i	$-0.919503\pi$
$103$	−16.9382	−	9.77929i	−1.66897	−	0.963582i	−0.700779	−	0.713378i	$-0.747164\pi$
$104$	30.6010	−	1.50752i	3.00067	−	0.147825i
$105$	2.23097	−	1.52783i	0.217721	−	0.149101i
$106$	4.82068	+	17.9910i	0.468226	+	1.74744i
$107$	−5.51934	+	3.18659i	−0.533575	+	0.308060i	−0.742471	−	0.669878i	$-0.766346\pi$
$107$	−5.51934	+	3.18659i	−0.533575	+	0.308060i	0.208896	+	0.977938i	$0.433013\pi$
$108$	−19.5896	+	18.4042i	−1.88501	+	1.77095i
$109$	−11.3751	+	11.3751i	−1.08954	+	1.08954i	−0.0939620	+	0.995576i	$0.529953\pi$
$109$	−11.3751	+	11.3751i	−1.08954	+	1.08954i	−0.995576	+	0.0939620i	$0.970047\pi$
$110$	−0.989820	−	0.989820i	−0.0943756	−	0.0943756i
$111$	−10.6794	−	9.15198i	−1.01365	−	0.868668i
$112$	−11.9895	+	3.21257i	−1.13290	+	0.303559i
$113$	−5.91873	+	3.41718i	−0.556787	+	0.321461i	−0.751855	−	0.659329i	$-0.770841\pi$
$113$	−5.91873	+	3.41718i	−0.556787	+	0.321461i	0.195068	+	0.980790i	$0.437507\pi$
$114$	−4.13590	+	0.318557i	−0.387363	+	0.0298356i
$115$	−1.53151	+	0.410366i	−0.142814	+	0.0382669i
$116$	49.4584			4.59210
$117$	0.636024	−	10.7979i	0.0588004	−	0.998270i
$118$	−4.63145			−0.426360
$119$	4.51778	−	1.21053i	0.414144	−	0.110970i
$120$	12.9827	+	18.9576i	1.18515	+	1.73059i
$121$	9.42921	−	5.44395i	0.857201	−	0.494905i
$122$	−15.7258	+	4.21372i	−1.42375	+	0.381492i
$123$	−6.11137	+	2.15267i	−0.551043	+	0.194100i
$124$	7.90362	+	7.90362i	0.709766	+	0.709766i
$125$	8.34857	−	8.34857i	0.746719	−	0.746719i
$126$	1.23039	+	7.93987i	0.109612	+	0.707340i
$127$	−11.5329	+	6.65853i	−1.02338	+	0.590849i	−0.915081	−	0.403269i	$-0.867874\pi$
$127$	−11.5329	+	6.65853i	−1.02338	+	0.590849i	−0.108299	+	0.994118i	$0.534541\pi$
$128$	−4.54548	−	16.9640i	−0.401768	−	1.49942i
$129$	−7.15041	−	3.42523i	−0.629559	−	0.301575i
$130$	−14.7357	−	3.18051i	−1.29241	−	0.278949i
$131$	−8.33050	−	4.80961i	−0.727839	−	0.420218i	0.0897921	−	0.995961i	$-0.471380\pi$
$131$	−8.33050	−	4.80961i	−0.727839	−	0.420218i	−0.817631	+	0.575743i	$0.804713\pi$
$132$	2.82927	−	0.996584i	0.246256	−	0.0867415i
$133$	−0.447115	+	0.774426i	−0.0387698	+	0.0671512i
$134$	14.4511	−	25.0300i	1.24838	−	2.16226i
$135$	7.14820	−	3.83493i	0.615219	−	0.330058i
$136$	10.2865	+	38.3897i	0.882059	+	3.29189i
$137$	−0.00812326	+	0.00812326i	−0.000694017	+	0.000694017i	−0.707454	−	0.706760i	$-0.750156\pi$
$137$	−0.00812326	+	0.00812326i	−0.000694017	+	0.000694017i	0.706760	+	0.707454i	$0.250156\pi$
$138$	0.866294	−	4.63095i	0.0737438	−	0.394212i
$139$	−3.71288	−	6.43089i	−0.314922	−	0.545461i	0.664499	−	0.747289i	$-0.268645\pi$
$139$	−3.71288	−	6.43089i	−0.314922	−	0.545461i	−0.979421	+	0.201828i	$0.935312\pi$
$140$	8.07551			0.682505
$141$	2.07333	−	2.41936i	0.174606	−	0.203747i
$142$	−8.93504	+	5.15865i	−0.749812	+	0.432904i
$143$	−0.551397	+	1.07384i	−0.0461102	+	0.0897990i
$144$	−36.7980	+	5.70237i	−3.06650	+	0.475197i
$145$	−14.4178	−	3.86324i	−1.19733	−	0.320825i
$146$	38.7941	+	22.3978i	3.21062	+	1.85365i
$147$	1.56208	+	0.748276i	0.128838	+	0.0617167i
$148$	−10.8714	−	40.5727i	−0.893625	−	3.33505i
$149$	1.58136	−	5.90173i	0.129550	−	0.483488i	−0.870411	−	0.492326i	$-0.836147\pi$
$149$	1.58136	−	5.90173i	0.129550	−	0.483488i	0.999961	+	0.00883816i	$0.00281331\pi$
$150$	3.94974	+	11.2132i	0.322495	+	0.915552i
$151$	1.79306	−	6.69178i	0.145917	−	0.544570i	−0.853796	−	0.520608i	$-0.825705\pi$
$151$	1.79306	−	6.69178i	0.145917	−	0.544570i	0.999713	−	0.0239617i	$-0.00762798\pi$
$152$	−6.58067	−	3.79935i	−0.533763	−	0.308168i
$153$	13.8659	−	2.14872i	1.12099	−	0.173714i
$154$	0.232073	−	0.866109i	0.0187010	−	0.0697930i
$155$	−1.68666	−	2.92137i	−0.135475	−	0.234650i
$156$	19.7885	−	25.5339i	1.58435	−	2.04435i
$157$	9.04041	−	15.6584i	0.721503	−	1.24968i	−0.238894	−	0.971046i	$-0.576785\pi$
$157$	9.04041	−	15.6584i	0.721503	−	1.24968i	0.960397	−	0.278634i	$-0.0898817\pi$
$158$	−12.5138	−	12.5138i	−0.995547	−	0.995547i
$159$	10.8635	+	5.20390i	0.861531	+	0.412696i
$160$			25.3656i			2.00533i
$161$	−0.718155	−	0.718155i	−0.0565985	−	0.0565985i
$162$	1.10075	+	24.0788i	0.0864830	+	1.89181i
$163$	24.0441	−	6.44260i	1.88328	−	0.504624i	0.883969	−	0.467546i	$-0.154862\pi$
$163$	24.0441	−	6.44260i	1.88328	−	0.504624i	0.999312	−	0.0370776i	$-0.0118049\pi$
$164$	−18.6916	−	5.00840i	−1.45957	−	0.391090i
$165$	−0.902615	+	0.0695215i	−0.0702685	+	0.00541224i
$166$			34.3587i			2.66675i
$167$	15.9545	−	15.9545i	1.23459	−	1.23459i	0.272412	−	0.962181i	$-0.412179\pi$
$167$	15.9545	−	15.9545i	1.23459	−	1.23459i	0.962181	−	0.272412i	$-0.0878213\pi$
$168$	−6.35846	+	13.2737i	−0.490566	+	1.02409i
$169$	1.27776	+	12.9371i	0.0982890	+	0.995158i
$170$		−	19.5555i		−	1.49984i
$171$	−1.58408	+	2.16507i	−0.121138	+	0.165567i
$172$	−11.8393	−	20.5063i	−0.902738	−	1.56359i
$173$	−11.6631			−0.886729			−0.443364	−	0.896341i	$-0.646215\pi$
$173$	−11.6631			−0.886729			−0.443364	+	0.896341i	$0.646215\pi$
$174$	28.8609	−	33.6778i	2.18794	−	2.55311i
$175$	2.47551	+	0.663310i	0.187131	+	0.0501415i
$176$	4.01406	+	1.07556i	0.302571	+	0.0810737i
$177$	−1.94906	+	2.27435i	−0.146500	+	0.170951i
$178$	3.27787			0.245687
$179$	7.45449	+	12.9116i	0.557175	+	0.965055i	0.997731	+	0.0673301i	$0.0214481\pi$
$179$	7.45449	+	12.9116i	0.557175	+	0.965055i	−0.440556	+	0.897725i	$0.645219\pi$
$180$	24.0852	+	2.61279i	1.79521	+	0.194746i
$181$		−	7.82099i		−	0.581329i	−0.956825	−	0.290665i	$-0.906124\pi$
$181$		−	7.82099i		−	0.581329i	0.956825	−	0.290665i	$-0.0938764\pi$
$182$	−2.95519	−	9.19312i	−0.219053	−	0.681440i
$183$	−4.54868	+	9.49569i	−0.336248	+	0.701942i
$184$	6.10251	−	6.10251i	0.449883	−	0.449883i
$185$			12.6767i			0.932008i
$186$	9.99390	−	0.769753i	0.732788	−	0.0564410i
$187$	−1.51254	−	0.405285i	−0.110608	−	0.0296374i
$188$	9.19150	−	2.46285i	0.670359	−	0.179622i
$189$	4.41680	+	2.73714i	0.321275	+	0.199097i
$190$	2.64376	+	2.64376i	0.191798	+	0.191798i
$191$			4.92215i			0.356154i	0.984017	+	0.178077i	$0.0569876\pi$
$191$			4.92215i			0.356154i	−0.984017	+	0.178077i	$0.943012\pi$
$192$	−29.1969	−	13.9861i	−2.10710	−	1.00936i
$193$	−15.0165	−	15.0165i	−1.08091	−	1.08091i	−0.996425	−	0.0844833i	$-0.973076\pi$
$193$	−15.0165	−	15.0165i	−1.08091	−	1.08091i	−0.0844833	−	0.996425i	$-0.526924\pi$
$194$	−16.4460	+	28.4853i	−1.18075	+	2.04512i
$195$	−7.76310	+	5.89778i	−0.555927	+	0.422349i
$196$	2.58641	+	4.47979i	0.184744	+	0.319985i
$197$	−6.31085	+	23.5524i	−0.449630	+	1.67804i	0.253784	+	0.967261i	$0.418325\pi$
$197$	−6.31085	+	23.5524i	−0.449630	+	1.67804i	−0.703414	+	0.710780i	$0.748342\pi$
$198$	0.972383	−	2.50808i	0.0691043	−	0.178242i
$199$	−15.1832	−	8.76601i	−1.07631	−	0.621406i	−0.146409	−	0.989224i	$-0.546772\pi$
$199$	−15.1832	−	8.76601i	−1.07631	−	0.621406i	−0.929898	+	0.367818i	$0.880105\pi$
$200$	−5.63646	+	21.0356i	−0.398558	+	1.48744i
$201$	−6.20996	−	17.6299i	−0.438017	−	1.24351i
$202$	4.24635	−	15.8476i	0.298772	−	1.11503i
$203$	−2.47462	−	9.23542i	−0.173684	−	0.648199i
$204$	37.7929	+	18.1038i	2.64603	+	1.26752i
$205$	5.05765	+	2.92003i	0.353241	+	0.203944i
$206$	−50.5971	−	13.5575i	−3.52527	−	0.944593i
$207$	−1.90954	−	2.37425i	−0.132722	−	0.165022i
$208$	42.6064	−	13.6961i	2.95422	−	0.949652i
$209$	0.259277	−	0.149693i	0.0179345	−	0.0103545i
$210$	4.71238	−	5.49887i	0.325185	−	0.379458i
$211$	−27.9681			−1.92540			−0.962702	−	0.270564i	$-0.912790\pi$
$211$	−27.9681			−1.92540			−0.962702	+	0.270564i	$0.912790\pi$
$212$	17.9872	+	31.1548i	1.23537	+	2.13972i
$213$	−1.22690	+	6.55862i	−0.0840656	+	0.449390i
$214$	−12.0694	+	12.0694i	−0.825049	+	0.825049i
$215$	1.84956	+	6.90264i	0.126139	+	0.470756i
$216$	−23.2588	+	37.5316i	−1.58256	+	2.55370i
$217$	1.08040	−	1.87130i	0.0733422	−	0.127032i
$218$	−21.5420	+	37.3118i	−1.45901	+	2.52707i
$219$	27.3246	−	9.62484i	1.84642	−	0.650386i
$220$	−2.34145	−	1.35183i	−0.157860	−	0.0911407i
$221$	−16.0546	+	5.16085i	−1.07995	+	0.347156i
$222$	−33.9711	−	16.2731i	−2.27999	−	1.09218i
$223$	−1.37171	−	5.11930i	−0.0918566	−	0.342813i	0.904668	−	0.426118i	$-0.140119\pi$
$223$	−1.37171	−	5.11930i	−0.0918566	−	0.342813i	−0.996524	+	0.0833047i	$0.973453\pi$
$224$	−14.0713	+	8.12406i	−0.940177	+	0.542811i
$225$	7.16859	+	2.77926i	0.477906	+	0.185284i
$226$	−12.9428	+	12.9428i	−0.860941	+	0.860941i
$227$	14.9272	+	14.9272i	0.990753	+	0.990753i	0.999958	−	0.00920467i	$-0.00292998\pi$
$227$	14.9272	+	14.9272i	0.990753	+	0.990753i	−0.00920467	+	0.999958i	$0.502930\pi$
$228$	−7.55683	+	2.66183i	−0.500463	+	0.176284i
$229$	11.7999	−	3.16177i	0.779757	−	0.208935i	0.153080	−	0.988214i	$-0.451081\pi$
$229$	11.7999	−	3.16177i	0.779757	−	0.208935i	0.626678	+	0.779278i	$0.284414\pi$
$230$	−3.67749	+	2.12320i	−0.242486	+	0.140000i
$231$	−0.327654	−	0.478449i	−0.0215581	−	0.0314796i
$232$	78.4778	−	21.0281i	5.15232	−	1.38056i
$233$	−23.1983			−1.51977			−0.759885	−	0.650058i	$-0.774745\pi$
$233$	−23.1983			−1.51977			−0.759885	+	0.650058i	$0.774745\pi$
$234$	−5.83947	−	28.3746i	−0.381738	−	1.85491i
$235$	−2.87182			−0.187337
$236$	−8.64059	+	2.31524i	−0.562454	+	0.150709i
$237$	−11.4113	+	0.878927i	−0.741246	+	0.0570925i
$238$	10.8482	−	6.26319i	0.703182	−	0.405983i
$239$	18.5767	−	4.97762i	1.20163	−	0.321976i	0.398157	−	0.917317i	$-0.369650\pi$
$239$	18.5767	−	4.97762i	1.20163	−	0.321976i	0.803472	+	0.595342i	$0.202983\pi$
$240$	25.4850	+	21.8399i	1.64505	+	1.40976i
$241$	12.9752	+	12.9752i	0.835805	+	0.835805i	0.988304	−	0.152498i	$-0.0487319\pi$
$241$	12.9752	+	12.9752i	0.835805	+	0.835805i	−0.152498	+	0.988304i	$0.548732\pi$
$242$	20.6193	−	20.6193i	1.32546	−	1.32546i
$243$	12.2875	+	9.59254i	0.788245	+	0.615362i
$244$	−27.2322	+	15.7225i	−1.74336	+	1.00653i
$245$	−0.404053	−	1.50795i	−0.0258140	−	0.0963393i
$246$	−14.3177	+	9.80510i	−0.912860	+	0.625150i
$247$	1.47275	−	2.86817i	0.0937091	−	0.182497i
$248$	15.9014	+	9.18066i	1.00974	+	0.582972i
$249$	16.8724	+	14.4592i	1.06925	+	0.916314i
$250$	15.8104	−	27.3844i	0.999936	−	1.73194i
$251$	5.51847	−	9.55827i	0.348323	−	0.603313i	−0.637629	−	0.770344i	$-0.720085\pi$
$251$	5.51847	−	9.55827i	0.348323	−	0.603313i	0.985952	+	0.167031i	$0.0534180\pi$
$252$	6.26456	+	14.1978i	0.394630	+	0.894378i
$253$	0.0880061	+	0.328443i	0.00553290	+	0.0206491i
$254$	−25.2196	+	25.2196i	−1.58242	+	1.58242i
$255$	−9.60306	−	8.22955i	−0.601367	−	0.515354i
$256$	−4.82685	−	8.36035i	−0.301678	−	0.522522i
$257$	3.55542			0.221781			0.110891	−	0.993833i	$-0.464630\pi$
$257$	3.55542			0.221781			0.110891	+	0.993833i	$0.464630\pi$
$258$	−20.8721	−	3.90446i	−1.29944	−	0.243081i
$259$	−7.03224	+	4.06006i	−0.436962	+	0.252280i
$260$	−29.0814	+	1.43266i	−1.80355	+	0.0888498i
$261$	−4.39250	−	28.3453i	−0.271889	−	1.75453i
$262$	−24.8845	−	6.66778i	−1.53737	−	0.411937i
$263$	−17.5890	−	10.1550i	−1.08458	−	0.626184i	−0.152454	−	0.988311i	$-0.548718\pi$
$263$	−17.5890	−	10.1550i	−1.08458	−	0.626184i	−0.932129	+	0.362126i	$0.882051\pi$
$264$	4.06561	−	2.78423i	0.250221	−	0.171358i
$265$	−2.81000	−	10.4871i	−0.172617	−	0.644215i
$266$	−0.619855	+	2.31333i	−0.0380058	+	0.141839i
$267$	1.37943	−	1.60966i	0.0844197	−	0.0985093i
$268$	14.4480	−	53.9208i	0.882554	−	3.29374i
$269$	−17.0651	−	9.85253i	−1.04048	−	0.600719i	−0.120508	−	0.992712i	$-0.538452\pi$
$269$	−17.0651	−	9.85253i	−1.04048	−	0.600719i	−0.919968	+	0.391993i	$0.871786\pi$
$270$	15.8338	−	14.8757i	0.963614	−	0.905308i
$271$	−0.664827	+	2.48117i	−0.0403854	+	0.150720i	−0.983174	−	0.182670i	$-0.941526\pi$
$271$	−0.664827	+	2.48117i	−0.0403854	+	0.150720i	0.942789	+	0.333390i	$0.108193\pi$
$272$	29.0273	+	50.2768i	1.76004	+	3.04848i
$273$	−5.75808	−	2.41755i	−0.348495	−	0.146317i
$274$	−0.0153837	+	0.0266453i	−0.000929362	+	0.00160970i
$275$	−0.606721	−	0.606721i	−0.0365866	−	0.0365866i
$276$	−0.698800	−	9.07270i	−0.0420628	−	0.546112i
$277$			19.2411i			1.15608i	0.816007	+	0.578042i	$0.196183\pi$
$277$			19.2411i			1.15608i	−0.816007	+	0.578042i	$0.803817\pi$
$278$	−14.0628	−	14.0628i	−0.843429	−	0.843429i
$279$	3.82774	−	5.23161i	0.229161	−	0.313208i
$280$	12.8138	−	3.43344i	0.765769	−	0.205187i
$281$	−6.17091	−	1.65349i	−0.368126	−	0.0986390i	0.0700136	−	0.997546i	$-0.477696\pi$
$281$	−6.17091	−	1.65349i	−0.368126	−	0.0986390i	−0.438139	+	0.898907i	$0.644362\pi$
$282$	3.68656	−	7.69595i	0.219532	−	0.458287i
$283$		−	28.1378i		−	1.67262i	−0.548258	−	0.836310i	$-0.684709\pi$
$283$		−	28.1378i		−	1.67262i	0.548258	−	0.836310i	$-0.315291\pi$
$284$	−14.0907	+	14.0907i	−0.836131	+	0.836131i
$285$	2.41084	−	0.185688i	0.142806	−	0.0109992i
$286$	−0.682083	+	3.16019i	−0.0403324	+	0.186866i
$287$			3.74089i			0.220818i
$288$	−44.5961	+	19.6773i	−2.62785	+	1.15950i
$289$	−2.43785	−	4.22247i	−0.143403	−	0.248381i
$290$	−39.9761			−2.34748
$291$	7.06722	+	20.0636i	0.414288	+	1.17615i
$292$	83.5721	+	22.3931i	4.89069	+	1.31046i
$293$	−15.4467	−	4.13894i	−0.902408	−	0.241799i	−0.222358	−	0.974965i	$-0.571375\pi$
$293$	−15.4467	−	4.13894i	−0.902408	−	0.241799i	−0.680050	+	0.733166i	$0.738042\pi$
$294$	4.55970	+	0.852967i	0.265927	+	0.0497460i
$295$	2.69970			0.157182
$296$	−34.5003	−	59.7563i	−2.00529	−	3.47326i
$297$	−0.822430	−	1.53298i	−0.0477222	−	0.0889528i
$298$		−	16.3637i		−	0.947921i
$299$	2.71361	+	2.45880i	0.156932	+	0.142196i
$300$	12.9742	+	18.9452i	0.749064	+	1.09380i
$301$	−3.23678	+	3.23678i	−0.186565	+	0.186565i
$302$		−	18.5542i		−	1.06768i
$303$	−5.99523	−	8.75439i	−0.344417	−	0.502927i
$304$	−10.7213	−	2.87278i	−0.614911	−	0.164765i
$305$	9.16665	−	2.45620i	0.524881	−	0.140641i
$306$	34.3811	−	15.1701i	1.96544	−	0.867218i
$307$	−12.6260	−	12.6260i	−0.720605	−	0.720605i	0.248123	−	0.968728i	$-0.420186\pi$
$307$	−12.6260	−	12.6260i	−0.720605	−	0.720605i	−0.968728	+	0.248123i	$0.920186\pi$
$308$		−	1.73185i		−	0.0986814i
$309$	−27.9505	+	19.1412i	−1.59005	+	1.08890i
$310$	−6.38831	−	6.38831i	−0.362832	−	0.362832i
$311$	−15.4537	+	26.7665i	−0.876296	+	1.51779i	−0.0209210	+	0.999781i	$0.506660\pi$
$311$	−15.4537	+	26.7665i	−0.876296	+	1.51779i	−0.855375	+	0.518009i	$0.826673\pi$
$312$	20.5431	−	48.9291i	1.16302	−	2.77007i
$313$	−5.69017	−	9.85567i	−0.321628	−	0.557075i	0.659196	−	0.751971i	$-0.270897\pi$
$313$	−5.69017	−	9.85567i	−0.321628	−	0.557075i	−0.980824	+	0.194896i	$0.937563\pi$
$314$	12.5331	−	46.7742i	0.707285	−	2.63962i
$315$	−0.717202	−	4.62819i	−0.0404098	−	0.260769i
$316$	−29.6018	−	17.0906i	−1.66523	−	0.961422i
$317$	−3.76686	+	14.0581i	−0.211568	+	0.789582i	0.775779	+	0.631005i	$0.217357\pi$
$317$	−3.76686	+	14.0581i	−0.211568	+	0.789582i	−0.987347	+	0.158577i	$0.949309\pi$
$318$	31.7106	+	5.93197i	1.77824	+	0.332649i
$319$	−0.828500	+	3.09200i	−0.0463871	+	0.173119i
$320$	7.55219	+	28.1852i	0.422180	+	1.57560i
$321$	0.847714	+	11.0061i	0.0473148	+	0.614300i
$322$	−2.35564	−	1.36003i	−0.131275	−	0.0757914i
$323$	4.03993	+	1.08250i	0.224788	+	0.0602317i
$324$	14.0904	+	44.3719i	0.782802	+	2.46510i
$325$	−9.03243	−	1.94953i	−0.501029	−	0.108140i
$326$	57.7352	−	33.3334i	3.19766	−	1.84617i
$327$	9.25707	+	26.2805i	0.511917	+	1.45332i
$328$	−31.7882			−1.75521
$329$	−0.919783	−	1.59311i	−0.0507093	−	0.0878310i
$330$	−2.28683	+	0.805516i	−0.125886	+	0.0443422i
$331$	18.0008	−	18.0008i	0.989415	−	0.989415i	−0.0105293	−	0.999945i	$-0.503352\pi$
$331$	18.0008	−	18.0008i	0.989415	−	0.989415i	0.999945	+	0.0105293i	$0.00335164\pi$
$332$	17.1757	+	64.1007i	0.942640	+	3.51798i
$333$	−22.2873	+	9.83391i	−1.22133	+	0.538895i
$334$	30.2142	−	52.3326i	1.65325	−	2.86351i
$335$	−8.42361	+	14.5901i	−0.460231	+	0.797143i
$336$	−3.95315	+	21.1324i	−0.215662	+	1.15286i
$337$	−11.1467	−	6.43554i	−0.607198	−	0.350566i	0.164670	−	0.986349i	$-0.447344\pi$
$337$	−11.1467	−	6.43554i	−0.607198	−	0.350566i	−0.771868	+	0.635783i	$0.780677\pi$
$338$	12.2731	+	32.5819i	0.667569	+	1.77222i
$339$	0.909055	+	11.8025i	0.0493731	+	0.641024i
$340$	−9.77568	−	36.4833i	−0.530161	−	1.97859i
$341$	−0.626510	+	0.361716i	−0.0339274	+	0.0195880i
$342$	−2.59719	+	6.69897i	−0.140440	+	0.362239i
$343$	0.707107	−	0.707107i	0.0381802	−	0.0381802i
$344$	−27.5045	−	27.5045i	−1.48294	−	1.48294i
$345$	−0.504967	+	2.69940i	−0.0271865	+	0.145331i
$346$	−30.1719	+	8.08453i	−1.62205	+	0.434627i
$347$	12.0276	−	6.94415i	0.645676	−	0.372781i	−0.141122	−	0.989992i	$-0.545071\pi$
$347$	12.0276	−	6.94415i	0.645676	−	0.372781i	0.786798	+	0.617211i	$0.211738\pi$
$348$	37.0085	−	77.2578i	1.98386	−	4.14145i
$349$	14.9551	−	4.00721i	0.800529	−	0.214501i	0.164713	−	0.986342i	$-0.447330\pi$
$349$	14.9551	−	4.00721i	0.800529	−	0.214501i	0.635816	+	0.771840i	$0.280664\pi$
$350$	6.86381			0.366886
$351$	−16.3913	−	9.07335i	−0.874902	−	0.484300i
$352$	5.43985			0.289945
$353$	12.4067	−	3.32436i	0.660340	−	0.176938i	0.0869406	−	0.996213i	$-0.472291\pi$
$353$	12.4067	−	3.32436i	0.660340	−	0.176938i	0.573400	+	0.819276i	$0.305624\pi$
$354$	−3.46560	+	7.23468i	−0.184195	+	0.384519i
$355$	5.20828	−	3.00700i	0.276427	−	0.159595i
$356$	6.11531	−	1.63859i	0.324111	−	0.0868452i
$357$	1.48959	−	7.96293i	0.0788377	−	0.421443i
$358$	28.2344	+	28.2344i	1.49223	+	1.49223i
$359$	4.50071	−	4.50071i	0.237538	−	0.237538i	−0.578292	−	0.815830i	$-0.696280\pi$
$359$	4.50071	−	4.50071i	0.237538	−	0.237538i	0.815830	+	0.578292i	$0.196280\pi$
$360$	39.3279	−	6.09441i	2.07276	−	0.321204i
$361$	15.7620	−	9.10018i	0.829577	−	0.478957i
$362$	−5.42129	−	20.2325i	−0.284937	−	1.06340i
$363$	−1.44823	−	18.8027i	−0.0760123	−	0.986887i
$364$	−10.1089	−	15.6737i	−0.529850	−	0.821525i
$365$	−22.6133	−	13.0558i	−1.18363	−	0.683371i
$366$	−5.18509	+	27.7179i	−0.271029	+	1.44884i
$367$	2.68459	−	4.64984i	0.140134	−	0.242720i	−0.787413	−	0.616426i	$-0.788580\pi$
$367$	2.68459	−	4.64984i	0.140134	−	0.242720i	0.927547	+	0.373706i	$0.121913\pi$
$368$	6.30317	−	10.9174i	0.328576	−	0.569110i
$369$	−1.21034	+	11.1572i	−0.0630080	+	0.580822i
$370$	8.78712	+	32.7940i	0.456821	+	1.70488i
$371$	4.91759	−	4.91759i	0.255308	−	0.255308i
$372$	18.2601	−	6.43197i	0.946744	−	0.333482i
$373$	−9.09066	−	15.7455i	−0.470696	−	0.815270i	0.528742	−	0.848783i	$-0.322664\pi$
$373$	−9.09066	−	15.7455i	−0.470696	−	0.815270i	−0.999438	+	0.0335126i	$0.989331\pi$
$374$	−4.19382			−0.216857
$375$	−6.79408	−	19.2881i	−0.350845	−	0.996035i
$376$	13.5374	−	7.81584i	0.698139	−	0.403071i
$377$	10.5500	+	32.8194i	0.543353	+	1.69029i
$378$	13.3234	+	4.01924i	0.685279	+	0.206727i
$379$	7.51896	+	2.01470i	0.386223	+	0.103488i	0.446705	−	0.894681i	$-0.352597\pi$
$379$	7.51896	+	2.01470i	0.386223	+	0.103488i	−0.0604825	+	0.998169i	$0.519264\pi$
$380$	6.25388	+	3.61068i	0.320817	+	0.185224i
$381$	1.77134	+	22.9977i	0.0907484	+	1.17821i
$382$	3.41189	+	12.7334i	0.174568	+	0.651496i
$383$	−0.0727676	+	0.271573i	−0.00371825	+	0.0138767i	−0.967760	−	0.251874i	$-0.918953\pi$
$383$	−0.0727676	+	0.271573i	−0.00371825	+	0.0138767i	0.964042	+	0.265751i	$0.0856198\pi$
$384$	−29.9003	−	5.59334i	−1.52584	−	0.285434i
$385$	−0.135277	+	0.504859i	−0.00689433	+	0.0257300i
$386$	−49.2559	−	28.4379i	−2.50706	−	1.44745i
$387$	−10.7010	+	8.60647i	−0.543960	+	0.437491i
$388$	−16.4425	+	61.3644i	−0.834743	+	3.11530i
$389$	18.5788	+	32.1795i	0.941984	+	1.63156i	0.761680	+	0.647953i	$0.224375\pi$
$389$	18.5788	+	32.1795i	0.941984	+	1.63156i	0.180304	+	0.983611i	$0.442292\pi$
$390$	−15.9946	+	20.6385i	−0.809918	+	1.04507i
$391$	−2.37511	+	4.11381i	−0.120115	+	0.208044i
$392$	6.00863	+	6.00863i	0.303481	+	0.303481i
$393$	−13.7465	+	9.41396i	−0.693419	+	0.474871i
$394$			65.3036i			3.28995i
$395$	7.29437	+	7.29437i	0.367020	+	0.367020i
$396$	0.560331	−	5.16525i	0.0281577	−	0.259564i
$397$	15.1375	−	4.05609i	0.759731	−	0.203569i	0.141901	−	0.989881i	$-0.454679\pi$
$397$	15.1375	−	4.05609i	0.759731	−	0.203569i	0.617830	+	0.786312i	$0.288012\pi$
$398$	−45.3545	−	12.1527i	−2.27342	−	0.609160i
$399$	0.875147	+	1.27791i	0.0438122	+	0.0639756i
$400$			31.8109i			1.59055i
$401$	6.47558	−	6.47558i	0.323375	−	0.323375i	−0.526685	−	0.850060i	$-0.676565\pi$
$401$	6.47558	−	6.47558i	0.323375	−	0.323375i	0.850060	+	0.526685i	$0.176565\pi$
$402$	−28.2854	−	41.3030i	−1.41075	−	2.06001i
$403$	−3.55873	+	6.93058i	−0.177273	+	0.345237i
$404$		−	31.6885i		−	1.57656i
$405$	−0.641632	−	14.0356i	−0.0318830	−	0.697436i
$406$	−12.8035	−	22.1763i	−0.635425	−	1.10059i
$407$	2.71861			0.134756
$408$	67.6648	+	12.6578i	3.34991	+	0.626654i
$409$	8.27140	+	2.21631i	0.408994	+	0.109590i	0.457449	−	0.889236i	$-0.348763\pi$
$409$	8.27140	+	2.21631i	0.408994	+	0.109590i	−0.0484551	+	0.998825i	$0.515430\pi$
$410$	15.1080	+	4.04817i	0.746130	+	0.199925i
$411$	0.00661072	+	0.0187676i	0.000326083	+	0.000925737i
$412$	−101.173			−4.98443
$413$	0.864654	+	1.49762i	0.0425468	+	0.0736933i
$414$	−6.58567	−	4.81844i	−0.323668	−	0.236813i
$415$		−	20.0278i		−	0.983128i
$416$	49.2320	−	31.7526i	2.41380	−	1.55680i
$417$	−12.8238	+	0.987719i	−0.627985	+	0.0483688i
$418$	0.566973	−	0.566973i	0.0277316	−	0.0277316i
$419$			13.0322i			0.636665i	0.947979	+	0.318332i	$0.103123\pi$
$419$			13.0322i			0.636665i	−0.947979	+	0.318332i	$0.896877\pi$
$420$	6.04271	−	12.6146i	0.294854	−	0.615528i
$421$	−16.9503	−	4.54181i	−0.826106	−	0.221355i	−0.179092	−	0.983832i	$-0.557316\pi$
$421$	−16.9503	−	4.54181i	−0.826106	−	0.221355i	−0.647014	+	0.762478i	$0.723983\pi$
$422$	−72.3522	+	19.3867i	−3.52205	+	0.943730i
$423$	−2.22781	−	5.04905i	−0.108320	−	0.245493i
$424$	41.7871	+	41.7871i	2.02936	+	2.02936i
$425$		−	11.9867i		−	0.581443i
$426$	1.37233	+	17.8173i	0.0664896	+	0.863252i
$427$	4.29842	+	4.29842i	0.208015	+	0.208015i
$428$	−16.4837	+	28.5506i	−0.796769	+	1.38004i
$429$	1.26482	+	1.66485i	0.0610662	+	0.0803799i
$430$	9.56943	+	16.5747i	0.461479	+	0.799305i
$431$	−4.47410	+	16.6976i	−0.215510	+	0.804293i	0.770477	+	0.637468i	$0.220018\pi$
$431$	−4.47410	+	16.6976i	−0.215510	+	0.804293i	−0.985986	+	0.166825i	$0.946648\pi$
$432$	−18.6275	+	61.7483i	−0.896218	+	2.97087i
$433$	15.4578	+	8.92456i	0.742854	+	0.428887i	0.823106	−	0.567888i	$-0.192239\pi$
$433$	15.4578	+	8.92456i	0.742854	+	0.428887i	−0.0802520	+	0.996775i	$0.525572\pi$
$434$	1.49780	−	5.58988i	0.0718969	−	0.268323i
$435$	−16.8232	+	19.6309i	−0.806609	+	0.941232i
$436$	−21.5374	+	80.3788i	−1.03146	+	3.84945i
$437$	−0.235060	−	0.877255i	−0.0112444	−	0.0419648i
$438$	64.0157	−	43.8396i	3.05879	−	2.09474i
$439$	3.94455	+	2.27739i	0.188263	+	0.108694i	0.591169	−	0.806548i	$-0.298667\pi$
$439$	3.94455	+	2.27739i	0.188263	+	0.108694i	−0.402906	+	0.915241i	$0.632000\pi$
$440$	−4.29003	−	1.14951i	−0.204519	−	0.0548007i
$441$	2.33773	−	1.88017i	0.111320	−	0.0895318i
$442$	−37.9551	+	24.4795i	−1.80534	+	1.16437i
$443$	7.52619	−	4.34525i	0.357580	−	0.206449i	−0.310439	−	0.950593i	$-0.600476\pi$
$443$	7.52619	−	4.34525i	0.357580	−	0.206449i	0.668019	+	0.744144i	$0.267143\pi$
$444$	−71.5125	−	13.3776i	−3.39383	−	0.634871i
$445$	−1.91069			−0.0905753
$446$	−7.09711	−	12.2926i	−0.336058	−	0.582069i
$447$	−8.03565	−	6.88633i	−0.380073	−	0.325712i
$448$	−13.2166	+	13.2166i	−0.624425	+	0.624425i
$449$	1.49509	+	5.57974i	0.0705576	+	0.263324i	0.992189	−	0.124741i	$-0.0398101\pi$
$449$	1.49509	+	5.57974i	0.0705576	+	0.263324i	−0.921632	+	0.388066i	$0.873143\pi$
$450$	20.4713	+	2.22075i	0.965028	+	0.104687i
$451$	0.626223	−	1.08465i	0.0294877	−	0.0510741i
$452$	−17.6764	+	30.6165i	−0.831430	+	1.44008i
$453$	−9.11138	−	7.80819i	−0.428090	−	0.366861i
$454$	48.9631	+	28.2689i	2.29795	+	1.32672i
$455$	1.72259	+	5.35872i	0.0807564	+	0.251220i
$456$	−10.8590	+	7.43655i	−0.508521	+	0.348248i
$457$	2.15145	+	8.02932i	0.100641	+	0.375596i	0.997814	−	0.0660824i	$-0.0210500\pi$
$457$	2.15145	+	8.02932i	0.100641	+	0.375596i	−0.897174	+	0.441678i	$0.854383\pi$
$458$	28.3341	−	16.3587i	1.32396	−	0.764391i
$459$	7.01908	−	23.2675i	0.327623	−	1.08603i
$460$	−5.79946	+	5.79946i	−0.270401	+	0.270401i
$461$	−19.6734	−	19.6734i	−0.916282	−	0.916282i	0.0804747	−	0.996757i	$-0.474356\pi$
$461$	−19.6734	−	19.6734i	−0.916282	−	0.916282i	−0.996757	+	0.0804747i	$0.974356\pi$
$462$	−1.17927	−	1.01060i	−0.0548648	−	0.0470175i
$463$	31.7704	−	8.51286i	1.47650	−	0.395626i	0.571343	−	0.820711i	$-0.306423\pi$
$463$	31.7704	−	8.51286i	1.47650	−	0.395626i	0.905153	+	0.425085i	$0.139756\pi$
$464$	102.778	−	59.3388i	4.77134	−	2.75474i
$465$	−5.82549	+	0.448693i	−0.270151	+	0.0208076i
$466$	−60.0129	+	16.0804i	−2.78004	+	0.744910i
$467$	−0.436253			−0.0201874			−0.0100937	−	0.999949i	$-0.503213\pi$
$467$	−0.436253			−0.0201874			−0.0100937	+	0.999949i	$0.503213\pi$
$468$	−25.0786	−	50.0175i	−1.15926	−	2.31206i
$469$	−10.7916			−0.498309
$470$	−7.42928	+	1.99067i	−0.342687	+	0.0918227i
$471$	−17.6950	−	25.8386i	−0.815341	−	1.19058i
$472$	−12.7260	+	7.34738i	−0.585763	+	0.338190i
$473$	1.48032	−	0.396651i	0.0680653	−	0.0182380i
$474$	−28.9114	+	10.1838i	−1.32794	+	0.467756i
$475$	1.62052	+	1.62052i	0.0743546	+	0.0743546i
$476$	17.1078	−	17.1078i	0.784133	−	0.784133i
$477$	16.2578	−	13.0757i	0.744392	−	0.598693i
$478$	44.6068	−	25.7538i	2.04027	−	1.17795i
$479$	−0.793639	−	2.96190i	−0.0362623	−	0.135333i	0.945422	−	0.325850i	$-0.105650\pi$
$479$	−0.793639	−	2.96190i	−0.0362623	−	0.135333i	−0.981684	+	0.190517i	$0.938984\pi$
$480$	39.6231	+	18.9805i	1.80854	+	0.866336i
$481$	24.6041	−	15.8686i	1.12185	−	0.723546i
$482$	42.5603	+	24.5722i	1.93857	+	1.11923i
$483$	−1.65919	+	0.584435i	−0.0754958	+	0.0265927i
$484$	28.1606	−	48.7756i	1.28003	−	2.21707i
$485$	9.58645	−	16.6042i	0.435298	−	0.753959i
$486$	38.4365	+	16.2981i	1.74352	+	0.739297i
$487$	−0.201212	−	0.750934i	−0.00911779	−	0.0340281i	0.961217	−	0.275793i	$-0.0889404\pi$
$487$	−0.201212	−	0.750934i	−0.00911779	−	0.0340281i	−0.970335	+	0.241765i	$0.922274\pi$
$488$	−36.5258	+	36.5258i	−1.65344	+	1.65344i
$489$	7.92779	−	42.3796i	0.358507	−	1.91647i
$490$	−2.09054	−	3.62091i	−0.0944408	−	0.163576i
$491$	42.8340			1.93307			0.966536	−	0.256529i	$-0.0825790\pi$
$491$	42.8340			1.93307			0.966536	+	0.256529i	$0.0825790\pi$
$492$	−21.8100	+	25.4500i	−0.983269	+	1.14738i
$493$	−38.7279	+	22.3596i	−1.74422	+	1.00702i
$494$	1.82181	−	8.44070i	0.0819671	−	0.379765i
$495$	−0.566807	+	1.46197i	−0.0254761	+	0.0657109i
$496$	25.9068	+	6.94171i	1.16325	+	0.311692i
$497$	3.33620	+	1.92615i	0.149649	+	0.0863998i
$498$	53.6709	+	25.7098i	2.40505	+	1.15208i
$499$	−0.290496	−	1.08414i	−0.0130044	−	0.0485330i	0.959119	−	0.283004i	$-0.0913309\pi$
$499$	−0.290496	−	1.08414i	−0.0130044	−	0.0485330i	−0.972123	+	0.234471i	$0.924664\pi$
$500$	15.8070	−	58.9927i	0.706912	−	2.63823i
$501$	−12.9837	−	36.8604i	−0.580071	−	1.64680i
$502$	7.65050	−	28.5521i	0.341459	−	1.27434i
$503$	15.8728	+	9.16418i	0.707734	+	0.408611i	0.810222	−	0.586124i	$-0.199347\pi$
$503$	15.8728	+	9.16418i	0.707734	+	0.408611i	−0.102487	+	0.994734i	$0.532680\pi$
$504$	15.9767	+	19.8648i	0.711658	+	0.884848i
$505$	−2.47522	+	9.23763i	−0.110146	+	0.411069i
$506$	0.455336	+	0.788664i	0.0202421	+	0.0350604i
$507$	21.1648	+	7.68453i	0.939961	+	0.341282i
$508$	−34.4434	+	59.6577i	−1.52818	+	2.64688i
$509$	−23.5804	−	23.5804i	−1.04518	−	1.04518i	−0.998930	−	0.0462530i	$-0.985272\pi$
$509$	−23.5804	−	23.5804i	−1.04518	−	1.04518i	−0.0462530	−	0.998930i	$-0.514728\pi$
$510$	−30.5472	−	14.6329i	−1.35265	−	0.647955i
$511$		−	16.7259i		−	0.739911i
$512$	6.55499	+	6.55499i	0.289692	+	0.289692i
$513$	2.19667	+	4.09452i	0.0969852	+	0.180778i
$514$	9.19772	−	2.46452i	0.405694	−	0.108705i
$515$	29.4933	+	7.90271i	1.29963	+	0.348235i
$516$	−40.8914	+	3.14955i	−1.80014	+	0.138651i
$517$			0.615884i			0.0270865i
$518$	−15.3777	+	15.3777i	−0.675659	+	0.675659i
$519$	−8.72721	+	18.2186i	−0.383082	+	0.799710i
$520$	−45.5356	+	14.6377i	−1.99687	+	0.641906i
$521$		−	18.7598i		−	0.821883i	−0.911662	−	0.410941i	$-0.865200\pi$
$521$		−	18.7598i		−	0.821883i	0.911662	−	0.410941i	$-0.134800\pi$
$522$	−31.0114	−	70.2832i	−1.35733	−	3.07621i
$523$	7.03248	+	12.1806i	0.307509	+	0.532621i	0.977817	−	0.209462i	$-0.0671712\pi$
$523$	7.03248	+	12.1806i	0.307509	+	0.532621i	−0.670308	+	0.742083i	$0.733838\pi$
$524$	−49.7585			−2.17371
$525$	2.88850	−	3.37059i	0.126065	−	0.147105i
$526$	−52.5410	−	14.0783i	−2.29090	−	0.613844i
$527$	−9.76199	−	2.61572i	−0.425239	−	0.113942i
$528$	4.68373	−	5.46545i	0.203833	−	0.237853i
$529$	−21.9685			−0.955152
$530$	−14.5387	−	25.1817i	−0.631520	−	1.09382i
$531$	2.09428	+	4.74642i	0.0908842	+	0.205977i
$532$			4.62569i			0.200549i
$533$	−0.663664	−	13.4716i	−0.0287465	−	0.583521i
$534$	2.45275	−	5.12029i	0.106141	−	0.221577i
$535$	7.03533	−	7.03533i	0.304164	−	0.304164i
$536$		−	91.7013i		−	3.96089i
$537$	25.7469	−	1.98308i	1.11106	−	0.0855763i
$538$	−50.9761	−	13.6590i	−2.19774	−	0.588881i
$539$	−0.323391	+	0.0866523i	−0.0139294	+	0.00373238i
$540$	22.1038	−	35.6679i	0.951194	−	1.53490i
$541$	−9.05905	−	9.05905i	−0.389479	−	0.389479i	0.485023	−	0.874502i	$-0.338811\pi$
$541$	−9.05905	−	9.05905i	−0.389479	−	0.389479i	−0.874502	+	0.485023i	$0.838811\pi$
$542$			6.87951i			0.295500i
$543$	−12.2170	−	5.85225i	−0.524281	−	0.251144i
$544$	53.7364	+	53.7364i	2.30393	+	2.30393i
$545$	12.5569	−	21.7492i	0.537879	−	0.931634i
$546$	−16.5717	−	2.26276i	−0.709201	−	0.0968373i
$547$	5.48121	+	9.49373i	0.234359	+	0.405922i	0.959086	−	0.283114i	$-0.0913674\pi$
$547$	5.48121	+	9.49373i	0.234359	+	0.405922i	−0.724727	+	0.689036i	$0.758034\pi$
$548$	−0.0153804	+	0.0574006i	−0.000657020	+	0.00245203i
$549$	11.4293	+	14.2108i	0.487792	+	0.606502i
$550$	−1.99012	−	1.14900i	−0.0848591	−	0.0489934i
$551$	2.21288	−	8.25859i	0.0942719	−	0.351828i
$552$	−4.96623	−	14.0989i	−0.211377	−	0.600091i
$553$	−1.71024	+	6.38269i	−0.0727267	+	0.271420i
$554$	13.3374	+	49.7757i	0.566651	+	2.11477i
$555$	19.8019	+	9.48565i	0.840546	+	0.402643i
$556$	−33.2659	−	19.2060i	−1.41079	−	0.814518i
$557$	−0.173875	−	0.0465896i	−0.00736731	−	0.00197406i	0.255134	−	0.966906i	$-0.417881\pi$
$557$	−0.173875	−	0.0465896i	−0.00736731	−	0.00197406i	−0.262501	+	0.964932i	$0.584547\pi$
$558$	6.27578	−	16.1872i	0.265675	−	0.685260i
$559$	11.0820	−	12.2305i	0.468720	−	0.517294i
$560$	16.7815	−	9.68878i	0.709146	−	0.409425i
$561$	−1.76489	+	2.05945i	−0.0745136	+	0.0869499i
$562$	−17.1100			−0.721743
$563$	5.83755	+	10.1109i	0.246023	+	0.426125i	0.962419	−	0.271569i	$-0.0875426\pi$
$563$	5.83755	+	10.1109i	0.246023	+	0.426125i	−0.716395	+	0.697694i	$0.754209\pi$
$564$	3.03061	−	16.2007i	0.127612	−	0.682173i
$565$	7.54441	−	7.54441i	0.317396	−	0.317396i
$566$	−19.5043	−	72.7912i	−0.819829	−	3.05964i
$567$	7.58060	−	4.85124i	0.318355	−	0.203733i
$568$	−16.3675	+	28.3493i	−0.686763	+	1.18951i
$569$	−6.22853	+	10.7881i	−0.261114	+	0.452262i	−0.966538	−	0.256523i	$-0.917423\pi$
$569$	−6.22853	+	10.7881i	−0.261114	+	0.452262i	0.705425	+	0.708785i	$0.250756\pi$
$570$	6.10801	−	2.15149i	0.255837	−	0.0901161i
$571$	2.12390	+	1.22624i	0.0888825	+	0.0513163i	0.543782	−	0.839226i	$-0.316992\pi$
$571$	2.12390	+	1.22624i	0.0888825	+	0.0513163i	−0.454900	+	0.890543i	$0.650325\pi$
$572$	0.307244	+	6.23672i	0.0128465	+	0.260770i
$573$	7.68877	+	3.68312i	0.321203	+	0.153865i
$574$	2.59308	+	9.67751i	0.108233	+	0.403932i
$575$	−2.25416	+	1.30144i	−0.0940048	+	0.0542737i
$576$	−43.6946	+	35.1423i	−1.82061	+	1.46426i
$577$	26.3001	−	26.3001i	1.09489	−	1.09489i	0.0998906	−	0.994998i	$-0.468151\pi$
$577$	26.3001	−	26.3001i	1.09489	−	1.09489i	0.994998	−	0.0998906i	$-0.0318493\pi$
$578$	−9.23349	−	9.23349i	−0.384063	−	0.384063i
$579$	−34.6933	+	12.2204i	−1.44180	+	0.507863i
$580$	−74.5807	+	19.9838i	−3.09679	+	0.829783i
$581$	11.1102	−	6.41448i	0.460929	−	0.266118i
$582$	32.1901	+	47.0048i	1.33432	+	1.94841i
$583$	−2.24903	+	0.602625i	−0.0931452	+	0.0249582i
$584$	142.128			5.88131
$585$	3.40385	+	16.5397i	0.140732	+	0.683833i
$586$	−42.8290			−1.76925
$587$	11.0837	−	2.96986i	0.457472	−	0.122579i	−0.0227217	−	0.999742i	$-0.507233\pi$
$587$	11.0837	−	2.96986i	0.457472	−	0.122579i	0.480193	+	0.877163i	$0.340566\pi$
$588$	8.93313	−	0.688050i	0.368396	−	0.0283747i
$589$	1.67338	−	0.966124i	0.0689503	−	0.0398085i
$590$	6.98399	−	1.87135i	0.287526	−	0.0770424i
$591$	32.0684	+	27.4817i	1.31912	+	1.13045i
$592$	−71.2696	−	71.2696i	−2.92916	−	2.92916i
$593$	19.6866	−	19.6866i	0.808432	−	0.808432i	−0.175964	−	0.984397i	$-0.556304\pi$
$593$	19.6866	−	19.6866i	0.808432	−	0.808432i	0.984397	+	0.175964i	$0.0563044\pi$
$594$	−3.19021	−	3.39568i	−0.130896	−	0.139326i
$595$	−6.32345	+	3.65085i	−0.259236	+	0.149670i
$596$	−8.18010	−	30.5286i	−0.335070	−	1.25050i
$597$	−25.0544	+	17.1579i	−1.02541	+	0.702226i
$598$	8.72437	+	4.47980i	0.356766	+	0.183193i
$599$	23.4230	+	13.5233i	0.957039	+	0.552547i	0.895260	−	0.445543i	$-0.146989\pi$
$599$	23.4230	+	13.5233i	0.957039	+	0.552547i	0.0617786	+	0.998090i	$0.480323\pi$
$600$	28.6415	+	24.5450i	1.16929	+	1.00205i
$601$	−0.995154	+	1.72366i	−0.0405932	+	0.0703095i	−0.885608	−	0.464433i	$-0.846258\pi$
$601$	−0.995154	+	1.72366i	−0.0405932	+	0.0703095i	0.845015	+	0.534743i	$0.179591\pi$
$602$	−6.12976	+	10.6171i	−0.249830	+	0.432719i
$603$	−32.1859	−	3.49156i	−1.31071	−	0.142187i
$604$	−9.27516	−	34.6154i	−0.377401	−	1.40848i
$605$	−12.0191	+	12.0191i	−0.488646	+	0.488646i
$606$	−21.5777	−	18.4915i	−0.876534	−	0.751165i
$607$	2.13604	+	3.69974i	0.0866993	+	0.150168i	0.906114	−	0.423033i	$-0.139035\pi$
$607$	2.13604	+	3.69974i	0.0866993	+	0.150168i	−0.819415	+	0.573201i	$0.805701\pi$
$608$	−14.5296			−0.589251
$609$	−16.2781	−	3.04509i	−0.659623	−	0.123393i
$610$	22.0111	−	12.7081i	0.891205	−	0.514537i
$611$	3.59494	+	5.57391i	0.145436	+	0.225496i
$612$	56.5590	−	45.4888i	2.28626	−	1.83878i
$613$	−18.1084	−	4.85213i	−0.731392	−	0.195976i	−0.126143	−	0.992012i	$-0.540260\pi$
$613$	−18.1084	−	4.85213i	−0.731392	−	0.195976i	−0.605249	+	0.796036i	$0.706926\pi$
$614$	−41.4149	−	23.9109i	−1.67137	−	0.964966i
$615$	8.34583	−	5.71544i	0.336536	−	0.230469i
$616$	−0.736326	−	2.74801i	−0.0296674	−	0.110720i
$617$	−3.35380	+	12.5166i	−0.135019	+	0.503898i	0.864979	+	0.501808i	$0.167332\pi$
$617$	−3.35380	+	12.5166i	−0.135019	+	0.503898i	−0.999998	+	0.00208932i	$0.999335\pi$
$618$	−59.0384	+	68.8919i	−2.37487	+	2.77124i
$619$	−3.33774	+	12.4566i	−0.134155	+	0.500673i	0.865845	+	0.500312i	$0.166782\pi$
$619$	−3.33774	+	12.4566i	−0.134155	+	0.500673i	−1.00000		0.000360863i	$0.999885\pi$
$620$	−15.1117	−	8.72476i	−0.606902	−	0.350395i
$621$	−5.13763	+	1.20626i	−0.206166	+	0.0484054i
$622$	−21.4241	+	79.9558i	−0.859028	+	3.20593i
$623$	−0.611952	−	1.05993i	−0.0245173	−	0.0424653i
$624$	10.4870	−	76.8028i	0.419815	−	3.07457i
$625$	−2.80886	+	4.86509i	−0.112354	+	0.194603i
$626$	−21.5519	−	21.5519i	−0.861387	−	0.861387i
$627$	−0.0398222	−	0.517022i	−0.00159035	−	0.0206479i
$628$		−	93.5287i		−	3.73220i
$629$	26.8552	+	26.8552i	1.07079	+	1.07079i
$630$	−5.06350	−	11.4758i	−0.201735	−	0.457205i
$631$	−16.0630	+	4.30407i	−0.639458	+	0.171342i	−0.563958	−	0.825803i	$-0.690722\pi$
$631$	−16.0630	+	4.30407i	−0.639458	+	0.171342i	−0.0755002	+	0.997146i	$0.524055\pi$
$632$	−54.2368	−	14.5327i	−2.15742	−	0.578080i
$633$	−20.9279	+	43.6883i	−0.831808	+	1.73646i
$634$			38.9788i			1.54805i
$635$	14.7006	−	14.7006i	0.583377	−	0.583377i
$636$	62.1256	−	4.78506i	2.46344	−	0.189740i
$637$	−2.42098	+	2.67187i	−0.0959225	+	0.105863i
$638$			8.57317i			0.339415i
$639$	9.32702	+	6.82417i	0.368971	+	0.269960i
$640$	13.7087	+	23.7442i	0.541884	+	0.938571i
$641$	−35.3166			−1.39492			−0.697460	−	0.716624i	$-0.745687\pi$
$641$	−35.3166			−1.39492			−0.697460	+	0.716624i	$0.745687\pi$
$642$	9.82211	+	27.8846i	0.387648	+	1.10052i
$643$	29.2833	+	7.84644i	1.15482	+	0.309433i	0.784895	−	0.619628i	$-0.212717\pi$
$643$	29.2833	+	7.84644i	1.15482	+	0.309433i	0.369925	+	0.929062i	$0.379383\pi$
$644$	−5.07463	−	1.35974i	−0.199968	−	0.0535813i
$645$	12.1664	+	2.27593i	0.479053	+	0.0896145i
$646$	11.2015			0.440716
$647$	6.32665	+	10.9581i	0.248726	+	0.430807i	0.963173	−	0.268883i	$-0.0866546\pi$
$647$	6.32665	+	10.9581i	0.248726	+	0.430807i	−0.714446	+	0.699690i	$0.753321\pi$
$648$	41.2233	+	64.4160i	1.61941	+	2.53050i
$649$		−	0.578970i		−	0.0227265i
$650$	−24.7178	+	1.21769i	−0.969514	+	0.0477619i
$651$	−2.11468	−	3.08792i	−0.0828810	−	0.121025i
$652$	91.0495	−	91.0495i	3.56577	−	3.56577i
$653$		−	28.4430i		−	1.11306i	−0.830827	−	0.556530i	$-0.812132\pi$
$653$		−	28.4430i		−	1.11306i	0.830827	−	0.556530i	$-0.187868\pi$
$654$	42.1645	+	61.5697i	1.64876	+	2.40757i
$655$	14.5053	+	3.88668i	0.566769	+	0.151865i
$656$	−44.8513	+	12.0179i	−1.75115	+	0.469219i
$657$	5.41158	−	49.8851i	0.211126	−	1.94620i
$658$	−3.48374	−	3.48374i	−0.135810	−	0.135810i
$659$		−	6.11194i		−	0.238087i	−0.992889	−	0.119044i	$-0.962017\pi$
$659$		−	6.11194i		−	0.238087i	0.992889	−	0.119044i	$-0.0379828\pi$
$660$	−3.86372	+	2.64597i	−0.150395	+	0.102994i
$661$	−23.9343	−	23.9343i	−0.930935	−	0.930935i	0.0668296	−	0.997764i	$-0.478712\pi$
$661$	−23.9343	−	23.9343i	−0.930935	−	0.930935i	−0.997764	+	0.0668296i	$0.978712\pi$
$662$	34.0896	−	59.0450i	1.32493	−	2.29485i
$663$	−3.95162	+	28.9402i	−0.153468	+	1.12395i
$664$	54.5069	+	94.4088i	2.11528	+	3.66377i
$665$	0.361317	−	1.34845i	0.0140113	−	0.0522907i
$666$	−50.8395	+	40.8888i	−1.96999	+	1.58441i
$667$	8.40962	+	4.85530i	0.325622	+	0.187998i
$668$	30.2079	−	112.737i	1.16878	−	4.36194i
$669$	−9.02315	−	1.68793i	−0.348855	−	0.0652590i
$670$	−11.6780	+	43.5830i	−0.451161	+	1.68376i
$671$	−0.526749	−	1.96586i	−0.0203349	−	0.0758910i
$672$	2.16120	+	28.0595i	0.0833702	+	1.08242i
$673$	−2.96421	−	1.71139i	−0.114262	−	0.0659691i	0.441780	−	0.897123i	$-0.354347\pi$
$673$	−2.96421	−	1.71139i	−0.114262	−	0.0659691i	−0.556042	+	0.831154i	$0.687681\pi$
$674$	−33.2969	−	8.92187i	−1.28255	−	0.343658i
$675$	9.70550	−	9.11824i	0.373565	−	0.350961i
$676$	39.1846	+	54.6505i	1.50710	+	2.10194i
$677$	26.6098	−	15.3632i	1.02270	−	0.590456i	0.107815	−	0.994171i	$-0.465615\pi$
$677$	26.6098	−	15.3632i	1.02270	−	0.590456i	0.914885	+	0.403715i	$0.132281\pi$
$678$	10.5328	+	29.9024i	0.404511	+	1.14839i
$679$	12.2813			0.471314
$680$	−31.0230	−	53.7334i	−1.18968	−	2.06058i
$681$	34.4871	−	12.1478i	1.32155	−	0.465504i
$682$	−1.37002	+	1.37002i	−0.0524608	+	0.0524608i
$683$	−6.19496	−	23.1199i	−0.237044	−	0.884659i	−0.977217	−	0.212243i	$-0.931923\pi$
$683$	−6.19496	−	23.1199i	−0.237044	−	0.884659i	0.740173	−	0.672416i	$-0.234743\pi$
$684$	−1.49662	+	13.7961i	−0.0572246	+	0.527508i
$685$	0.00896722	−	0.0155317i	0.000342620	−	0.000593435i
$686$	1.33911	−	2.31940i	0.0511273	−	0.0885551i
$687$	3.89064	−	20.7982i	0.148437	−	0.793500i
$688$	−49.2057	−	28.4089i	−1.87595	−	1.08308i
$689$	−16.8367	+	18.5816i	−0.641428	+	0.707901i
$690$	0.564824	+	7.33326i	0.0215025	+	0.279172i
$691$	4.24027	+	15.8249i	0.161308	+	0.602008i	0.998482	+	0.0550725i	$0.0175390\pi$
$691$	4.24027	+	15.8249i	0.161308	+	0.602008i	−0.837175	+	0.546935i	$0.815794\pi$
$692$	−52.2482	+	30.1655i	−1.98618	+	1.14672i
$693$	−0.992549	+	0.153809i	−0.0377038	+	0.00584273i
$694$	26.3014	−	26.3014i	0.998387	−	0.998387i
$695$	8.19725	+	8.19725i	0.310940	+	0.310940i
$696$	25.8756	−	138.323i	0.980811	−	5.24312i
$697$	16.9005	−	4.52848i	0.640152	−	0.171528i
$698$	35.9105	−	20.7330i	1.35923	−	0.784754i
$699$	−17.3587	+	36.2375i	−0.656566	+	1.37063i
$700$	12.8053	−	3.43118i	0.483997	−	0.129687i
$701$	−7.13726			−0.269571			−0.134785	−	0.990875i	$-0.543034\pi$
$701$	−7.13726			−0.269571			−0.134785	+	0.990875i	$0.543034\pi$
$702$	−48.6929	−	12.1104i	−1.83780	−	0.457076i
$703$	−7.26126			−0.273864
$704$	6.04451	−	1.61962i	0.227811	−	0.0610418i
$705$	−2.14892	+	4.48601i	−0.0809329	+	0.168953i
$706$	29.7911	−	17.1999i	1.12120	−	0.647327i
$707$	−5.91722	+	1.58552i	−0.222540	+	0.0596294i
$708$	−2.84896	+	15.2297i	−0.107071	+	0.572367i
$709$	−15.8174	−	15.8174i	−0.594036	−	0.594036i	0.344683	−	0.938719i	$-0.387986\pi$
$709$	−15.8174	−	15.8174i	−0.594036	−	0.594036i	−0.938719	+	0.344683i	$0.887986\pi$
$710$	11.3892	−	11.3892i	0.427429	−	0.427429i
$711$	−7.16587	+	18.4831i	−0.268741	+	0.693169i
$712$	9.00675	−	5.20005i	0.337542	−	0.194880i
$713$	0.567993	+	2.11978i	0.0212715	+	0.0793863i
$714$	−1.66617	−	21.6323i	−0.0623547	−	0.809567i
$715$	0.397590	−	1.84209i	0.0148690	−	0.0688902i
$716$	66.7892	+	38.5607i	2.49603	+	1.44108i
$717$	6.12509	−	32.7429i	0.228746	−	1.22281i
$718$	8.52336	−	14.7629i	0.318089	−	0.550946i
$719$	−24.6534	+	42.7010i	−0.919419	+	1.59248i	−0.119118	+	0.992880i	$0.538007\pi$
$719$	−24.6534	+	42.7010i	−0.919419	+	1.59248i	−0.800300	+	0.599600i	$0.795327\pi$
$720$	53.1855	−	23.4672i	1.98211	−	0.874573i
$721$	5.06213	+	18.8921i	0.188524	+	0.703580i
$722$	34.4675	−	34.4675i	1.28275	−	1.28275i
$723$	29.9773	−	10.5592i	1.11487	−	0.392702i
$724$	−20.2283	−	35.0364i	−0.751778	−	1.30212i
$725$	−24.5038			−0.910048
$726$	−16.7800	−	47.6379i	−0.622765	−	1.76801i
$727$	43.6827	−	25.2202i	1.62010	−	0.935366i	0.633209	−	0.773981i	$-0.281737\pi$
$727$	43.6827	−	25.2202i	1.62010	−	0.935366i	0.986892	−	0.161385i	$-0.0515960\pi$
$728$	−22.7041	−	20.5722i	−0.841472	−	0.762456i
$729$	24.1787	−	12.0162i	0.895509	−	0.445044i
$730$	−67.5494	−	18.0998i	−2.50012	−	0.669904i
$731$	18.5413	+	10.7048i	0.685775	+	0.395932i
$732$	4.18258	+	54.3035i	0.154593	+	2.00711i
$733$	4.56269	+	17.0282i	0.168527	+	0.628950i	0.997564	+	0.0697568i	$0.0222223\pi$
$733$	4.56269	+	17.0282i	0.168527	+	0.628950i	−0.829037	+	0.559193i	$0.811111\pi$
$734$	3.72177	−	13.8898i	0.137373	−	0.512682i
$735$	−2.65787	−	0.497198i	−0.0980372	−	0.0183394i
$736$	4.27103	−	15.9397i	0.157432	−	0.587545i
$737$	3.12896	+	1.80650i	0.115257	+	0.0665435i
$738$	4.60277	+	29.7022i	0.169430	+	1.09335i
$739$	−11.6469	+	43.4670i	−0.428439	+	1.59896i	0.327856	+	0.944728i	$0.393674\pi$
$739$	−11.6469	+	43.4670i	−0.428439	+	1.59896i	−0.756296	+	0.654230i	$0.772993\pi$
$740$	32.7871	+	56.7889i	1.20528	+	2.08760i
$741$	−3.37828	−	4.44674i	−0.124104	−	0.163355i
$742$	9.31284	−	16.1303i	0.341885	−	0.592162i
$743$	10.7065	+	10.7065i	0.392785	+	0.392785i	0.875679	−	0.482894i	$-0.160414\pi$
$743$	10.7065	+	10.7065i	0.392785	+	0.392785i	−0.482894	+	0.875679i	$0.660414\pi$
$744$	26.2395	−	17.9695i	0.961987	−	0.658794i
$745$			9.53845i			0.349462i
$746$	−34.4314	−	34.4314i	−1.26062	−	1.26062i
$747$	35.2116	−	15.5366i	1.28832	−	0.568453i
$748$	−7.82412	+	2.09647i	−0.286078	+	0.0766544i
$749$	6.15603	+	1.64950i	0.224936	+	0.0602715i
$750$	−30.9460	−	45.1881i	−1.12999	−	1.65003i
$751$			32.9990i			1.20415i	0.798439	+	0.602076i	$0.205659\pi$
$751$			32.9990i			1.20415i	−0.798439	+	0.602076i	$0.794341\pi$
$752$	16.1457	−	16.1457i	0.588773	−	0.588773i
$753$	−10.8014	−	15.7725i	−0.393626	−	0.574782i
$754$	50.0419	+	77.5893i	1.82242	+	2.82564i
$755$			10.8154i			0.393611i
$756$	26.8657	+	0.838153i	0.977095	+	0.0304833i
$757$	12.5891	+	21.8050i	0.457559	+	0.792515i	0.998831	−	0.0483319i	$-0.0153905\pi$
$757$	12.5891	+	21.8050i	0.457559	+	0.792515i	−0.541272	+	0.840847i	$0.682057\pi$
$758$	20.8477			0.757223
$759$	0.578906	+	0.108294i	0.0210130	+	0.00393082i
$760$	11.4584	+	3.07028i	0.415642	+	0.111371i
$761$	12.9738	+	3.47632i	0.470299	+	0.126016i	0.486182	−	0.873858i	$-0.338389\pi$
$761$	12.9738	+	3.47632i	0.470299	+	0.126016i	−0.0158827	+	0.999874i	$0.505056\pi$
$762$	20.5237	+	58.2662i	0.743497	+	2.11076i
$763$	16.0868			0.582382
$764$	12.7307	+	22.0502i	0.460580	+	0.797748i
$765$	−20.0409	+	8.84274i	−0.724581	+	0.319710i
$766$			0.752986i			0.0272065i
$767$	−3.37947	−	5.23982i	−0.122025	−	0.189199i
$768$	−16.6713	+	1.28406i	−0.601574	+	0.0463346i
$769$	−8.00155	+	8.00155i	−0.288543	+	0.288543i	−0.836504	−	0.547961i	$-0.815404\pi$
$769$	−8.00155	+	8.00155i	−0.288543	+	0.288543i	0.547961	+	0.836504i	$0.315404\pi$
$770$			1.39982i			0.0504459i
$771$	2.66044	−	5.55384i	0.0958133	−	0.200017i
$772$	−106.109	−	28.4319i	−3.81896	−	1.02329i
$773$	3.51144	−	0.940887i	0.126298	−	0.0338414i	−0.195117	−	0.980780i	$-0.562508\pi$
$773$	3.51144	−	0.940887i	0.126298	−	0.0338414i	0.321414	+	0.946939i	$0.395842\pi$
$774$	−21.7171	+	29.6821i	−0.780606	+	1.06690i
$775$	−3.91579	−	3.91579i	−0.140659	−	0.140659i
$776$			104.360i			3.74632i
$777$	1.08008	+	14.0229i	0.0387476	+	0.503070i
$778$	70.3685	+	70.3685i	2.52283	+	2.52283i
$779$	−1.67261	+	2.89704i	−0.0599274	+	0.103797i
$780$	−19.5230	+	46.4994i	−0.699035	+	1.66495i
$781$	−0.644874	−	1.11695i	−0.0230754	−	0.0399678i
$782$	−3.29272	+	12.2886i	−0.117748	+	0.439440i
$783$	−47.5643	−	14.3487i	−1.69981	−	0.512780i
$784$	10.7495	+	6.20621i	0.383910	+	0.221650i
$785$	−7.30561	+	27.2649i	−0.260749	+	0.973127i
$786$	−29.0361	+	33.8822i	−1.03568	+	1.20854i
$787$	−4.03335	+	15.0527i	−0.143773	+	0.536570i	0.856033	+	0.516920i	$0.172922\pi$
$787$	−4.03335	+	15.0527i	−0.143773	+	0.536570i	−0.999807	+	0.0196495i	$0.993745\pi$
$788$	32.6449	+	121.832i	1.16293	+	4.34010i
$789$	−29.0243	+	19.8766i	−1.03329	+	0.707625i
$790$	23.9265	+	13.8139i	0.851265	+	0.491478i
$791$	6.60148	+	1.76886i	0.234722	+	0.0628935i
$792$	−1.30699	−	8.43417i	−0.0464419	−	0.299695i
$793$	−16.2420	−	14.7168i	−0.576770	−	0.522610i
$794$	36.3485	−	20.9858i	1.28996	−	0.744760i
$795$	−18.4842	−	3.45778i	−0.655568	−	0.122635i
$796$	−90.6900			−3.21442
$797$	14.0955	+	24.4140i	0.499287	+	0.864790i	1.00000		0.000823630i	$-0.000262170\pi$
$797$	14.0955	+	24.4140i	0.499287	+	0.864790i	−0.500713	+	0.865613i	$0.666929\pi$
$798$	3.14978	+	2.69927i	0.111501	+	0.0955532i
$799$	−6.08389	+	6.08389i	−0.215232	+	0.215232i
$800$	10.7775	+	40.2223i	0.381044	+	1.42207i
$801$	−1.48221	−	3.35924i	−0.0523714	−	0.118693i
$802$	12.2633	−	21.2407i	0.433034	−	0.750036i
$803$	−2.79991	+	4.84958i	−0.0988066	+	0.171138i
$804$	−73.4173	−	62.9166i	−2.58923	−	2.21890i
$805$	1.37311	+	0.792767i	0.0483959	+	0.0279414i
$806$	−4.40218	+	20.3959i	−0.155060	+	0.718415i
$807$	−28.1598	+	19.2846i	−0.991272	+	0.678849i
$808$	−13.4729	−	50.2815i	−0.473974	−	1.76890i
$809$	13.6887	−	7.90320i	0.481270	−	0.277862i	−0.239675	−	0.970853i	$-0.577041\pi$
$809$	13.6887	−	7.90320i	0.481270	−	0.277862i	0.720946	+	0.692992i	$0.243708\pi$
$810$	−11.3890	−	35.8648i	−0.400168	−	1.26016i
$811$	−18.4069	+	18.4069i	−0.646354	+	0.646354i	−0.952110	−	0.305756i	$-0.901091\pi$
$811$	−18.4069	+	18.4069i	−0.646354	+	0.646354i	0.305756	+	0.952110i	$0.401091\pi$
$812$	−34.9724	−	34.9724i	−1.22729	−	1.22729i
$813$	3.37830	+	2.89511i	0.118482	+	0.101536i
$814$	7.03291	−	1.88446i	0.246503	−	0.0660504i
$815$	−33.6541	+	19.4302i	−1.17885	+	0.680611i
$816$	100.257	−	7.72200i	3.50969	−	0.270324i
$817$	−3.95386	+	1.05943i	−0.138328	+	0.0370649i
$818$	22.9340			0.801869
$819$	−8.08503	+	7.18556i	−0.282514	+	0.251084i
$820$	30.2096			1.05496
$821$	−40.2275	+	10.7789i	−1.40395	+	0.376187i	−0.879761	−	0.475416i	$-0.842298\pi$
$821$	−40.2275	+	10.7789i	−1.40395	+	0.376187i	−0.524188	+	0.851603i	$0.675631\pi$
$822$	0.0301108	+	0.0439685i	0.00105023	+	0.00153358i
$823$	36.7552	−	21.2206i	1.28121	−	0.739705i	0.304137	−	0.952628i	$-0.401632\pi$
$823$	36.7552	−	21.2206i	1.28121	−	0.739705i	0.977069	+	0.212924i	$0.0682986\pi$
$824$	−160.535	+	43.0154i	−5.59252	+	1.49851i
$825$	−1.40174	+	0.493750i	−0.0488023	+	0.0171902i
$826$	3.27493	+	3.27493i	0.113949	+	0.113949i
$827$	−8.03799	+	8.03799i	−0.279508	+	0.279508i	−0.832913	−	0.553404i	$-0.813328\pi$
$827$	−8.03799	+	8.03799i	−0.279508	+	0.279508i	0.553404	+	0.832913i	$0.313328\pi$
$828$	−14.6951	−	5.69730i	−0.510692	−	0.197995i
$829$	11.8986	−	6.86966i	0.413255	−	0.238593i	−0.278932	−	0.960311i	$-0.589980\pi$
$829$	11.8986	−	6.86966i	0.413255	−	0.238593i	0.692187	+	0.721718i	$0.256647\pi$
$830$	−13.8827	−	51.8111i	−0.481877	−	1.79839i
$831$	30.0560	+	14.3976i	1.04263	+	0.499448i
$832$	45.2506	−	49.9401i	1.56878	−	1.73136i
$833$	−4.05053	−	2.33857i	−0.140342	−	0.0810267i
$834$	−32.4899	+	11.4443i	−1.12503	+	0.396283i
$835$	−17.6120	+	30.5049i	−0.609490	+	1.05567i
$836$	0.774337	−	1.34119i	0.0267810	−	0.0463861i
$837$	−5.30797	−	9.89391i	−0.183470	−	0.341984i
$838$	9.03356	+	33.7137i	0.312059	+	1.16462i
$839$	14.4216	−	14.4216i	0.497889	−	0.497889i	−0.412891	−	0.910780i	$-0.635481\pi$
$839$	14.4216	−	14.4216i	0.497889	−	0.497889i	0.910780	+	0.412891i	$0.135481\pi$
$840$	4.22493	−	22.5852i	0.145774	−	0.779264i
$841$	31.2083	+	54.0544i	1.07615	+	1.86395i
$842$	−46.9979			−1.61965
$843$	−7.20042	+	8.40217i	−0.247996	+	0.289386i
$844$	−125.291	+	72.3370i	−4.31270	+	2.48994i
$845$	−7.15405	−	18.9921i	−0.246107	−	0.653349i
$846$	−9.26310	−	11.5174i	−0.318472	−	0.395976i
$847$	−10.5169	−	2.81800i	−0.361365	−	0.0968276i
$848$	74.7574	+	43.1612i	2.56718	+	1.48216i
$849$	−43.9534	−	21.0548i	−1.50848	−	0.722600i
$850$	−8.30888	−	31.0092i	−0.284992	−	1.06361i
$851$	2.13448	−	7.96599i	0.0731690	−	0.273071i
$852$	11.4670	+	32.5545i	0.392854	+	1.11530i
$853$	−9.99683	+	37.3087i	−0.342285	+	1.27742i	0.553467	+	0.832871i	$0.313304\pi$
$853$	−9.99683	+	37.3087i	−0.342285	+	1.27742i	−0.895752	+	0.444554i	$0.853362\pi$
$854$	14.0994	+	8.14027i	0.482470	+	0.278554i
$855$	1.51391	−	3.90486i	0.0517747	−	0.133543i
$856$	−14.0166	+	52.3107i	−0.479078	+	1.78794i
$857$	−12.3511	−	21.3928i	−0.421906	−	0.730763i	0.574220	−	0.818701i	$-0.305306\pi$
$857$	−12.3511	−	21.3928i	−0.421906	−	0.730763i	−0.996126	+	0.0879381i	$0.971972\pi$
$858$	4.42607	+	3.43016i	0.151104	+	0.117104i
$859$	11.7560	−	20.3621i	0.401111	−	0.694744i	−0.592749	−	0.805387i	$-0.701958\pi$
$859$	11.7560	−	20.3621i	0.401111	−	0.694744i	0.993860	+	0.110643i	$0.0352909\pi$
$860$	26.1387	+	26.1387i	0.891321	+	0.891321i
$861$	5.84356	+	2.79922i	0.199148	+	0.0953971i
$862$			46.2971i			1.57689i
$863$	15.2101	+	15.2101i	0.517757	+	0.517757i	0.916892	−	0.399135i	$-0.130690\pi$
$863$	15.2101	+	15.2101i	0.517757	+	0.517757i	−0.399135	+	0.916892i	$0.630690\pi$
$864$	−2.63269	+	84.3866i	−0.0895658	+	2.87089i
$865$	17.5873	−	4.71251i	0.597988	−	0.160230i
$866$	46.1749	+	12.3725i	1.56909	+	0.420435i
$867$	−8.42001	+	0.648528i	−0.285958	+	0.0220252i
$868$		−	11.1774i		−	0.379386i
$869$	1.56433	−	1.56433i	0.0530663	−	0.0530663i
$870$	−29.9131	+	62.4457i	−1.01415	+	2.11711i
$871$	38.8625	−	1.91451i	1.31681	−	0.0648708i
$872$			136.698i			4.62916i
$873$	36.6291	+	3.97355i	1.23971	+	0.134484i
$874$	−1.21618	−	2.10648i	−0.0411378	−	0.0712528i
$875$	−11.8067			−0.399138
$876$	97.5146	−	113.790i	3.29471	−	3.84460i
$877$	−5.12868	−	1.37422i	−0.173183	−	0.0464043i	0.171185	−	0.985239i	$-0.445240\pi$
$877$	−5.12868	−	1.37422i	−0.173183	−	0.0464043i	−0.344369	+	0.938835i	$0.611907\pi$
$878$	11.7830	+	3.15724i	0.397657	+	0.106552i
$879$	−18.0238	+	21.0319i	−0.607926	+	0.709389i
$880$	−6.48758			−0.218696
$881$	−17.9554	−	31.0996i	−0.604932	−	1.04777i	−0.992062	−	0.125747i	$-0.959867\pi$
$881$	−17.9554	−	31.0996i	−0.604932	−	1.04777i	0.387131	−	0.922025i	$-0.373466\pi$
$882$	4.74432	−	6.48435i	0.159749	−	0.218340i
$883$			33.5980i			1.13066i	0.824864	+	0.565331i	$0.191251\pi$
$883$			33.5980i			1.13066i	−0.824864	+	0.565331i	$0.808749\pi$
$884$	−58.5731	+	64.6432i	−1.97003	+	2.17419i
$885$	2.02012	−	4.21713i	0.0679055	−	0.141757i
$886$	16.4579	−	16.4579i	0.552914	−	0.552914i
$887$			4.35462i			0.146214i	0.997324	+	0.0731070i	$0.0232914\pi$
$887$			4.35462i			0.146214i	−0.997324	+	0.0731070i	$0.976709\pi$
$888$	−119.160	+	9.17795i	−3.99874	+	0.307992i
$889$	12.8633	+	3.44671i	0.431421	+	0.115599i
$890$	−4.94286	+	1.32444i	−0.165685	+	0.0443952i
$891$	−3.01004	+	0.137603i	−0.100840	+	0.00460987i
$892$	−19.3856	−	19.3856i	−0.649077	−	0.649077i
$893$		−	1.64499i		−	0.0550476i
$894$	−25.5613	−	12.2445i	−0.854897	−	0.409518i
$895$	−16.4579	−	16.4579i	−0.550129	−	0.550129i
$896$	−8.78120	+	15.2095i	−0.293359	+	0.508113i
$897$	5.87137	−	2.39901i	0.196039	−	0.0801007i
$898$	7.73545	+	13.3982i	0.258135	+	0.447103i
$899$	−5.34715	+	19.9558i	−0.178338	+	0.665565i
$900$	39.3021	−	6.09041i	1.31007	−	0.203014i
$901$	−28.1695	−	16.2637i	−0.938461	−	0.541821i
$902$	0.868160	−	3.24002i	0.0289066	−	0.107881i
$903$	2.63410	+	7.47811i	0.0876573	+	0.248856i
$904$	−15.0309	+	56.0960i	−0.499919	+	1.86572i
$905$	3.16010	+	11.7936i	0.105045	+	0.392034i
$906$	−28.9831	−	13.8837i	−0.962900	−	0.461254i
$907$	14.1538	+	8.17169i	0.469969	+	0.271336i	0.716227	−	0.697868i	$-0.245868\pi$
$907$	14.1538	+	8.17169i	0.469969	+	0.271336i	−0.246258	+	0.969204i	$0.579201\pi$
$908$	105.479	+	28.2629i	3.50043	+	0.937937i
$909$	−18.1611	+	2.81432i	−0.602366	+	0.0933450i
$910$	8.17078	+	12.6687i	0.270859	+	0.419963i
$911$	39.6696	−	22.9033i	1.31431	−	0.758819i	0.331506	−	0.943453i	$-0.392443\pi$
$911$	39.6696	−	22.9033i	1.31431	−	0.758819i	0.982807	+	0.184634i	$0.0591101\pi$
$912$	−12.5100	+	14.5979i	−0.414248	+	0.483386i
$913$	−4.29512			−0.142148
$914$	11.1314	+	19.2802i	0.368194	+	0.637731i
$915$	3.02241	−	16.1569i	0.0999179	−	0.534131i
$916$	44.6834	−	44.6834i	1.47638	−	1.47638i
$917$	2.48964	+	9.29146i	0.0822151	+	0.306831i
$918$	2.02965	−	65.0574i	0.0669886	−	2.14721i
$919$	2.05153	−	3.55335i	0.0676737	−	0.117214i	−0.830203	−	0.557461i	$-0.811776\pi$
$919$	2.05153	−	3.55335i	0.0676737	−	0.117214i	0.897877	+	0.440247i	$0.145109\pi$
$920$	−6.73652	+	11.6680i	−0.222097	+	0.384683i
$921$	−29.1706	+	10.2751i	−0.961202	+	0.338575i
$922$	−64.5313	−	37.2571i	−2.12522	−	1.22700i
$923$	−12.3560	−	6.34457i	−0.406702	−	0.208834i
$924$	−2.70529	−	1.29590i	−0.0889974	−	0.0426321i
$925$	5.38616	+	20.1014i	0.177096	+	0.660931i
$926$	76.2877	−	44.0447i	2.50697	−	1.44740i
$927$	8.98537	+	57.9836i	0.295118	+	1.90443i
$928$	109.850	−	109.850i	3.60601	−	3.60601i
$929$	28.5765	+	28.5765i	0.937565	+	0.937565i	0.998162	−	0.0605968i	$-0.0193004\pi$
$929$	28.5765	+	28.5765i	0.937565	+	0.937565i	−0.0605968	+	0.998162i	$0.519300\pi$
$930$	−14.7593	+	5.19882i	−0.483975	+	0.170476i
$931$	0.863760	−	0.231444i	0.0283086	−	0.00758526i
$932$	−103.923	+	60.0002i	−3.40412	+	1.96537i
$933$	30.2478	+	44.1685i	0.990267	+	1.44601i
$934$	−1.12857	+	0.302399i	−0.0369278	+	0.00989478i
$935$	2.44460			0.0799468
$936$	−61.0591	−	68.7024i	−1.99578	−	2.24561i
$937$	−29.9872			−0.979640			−0.489820	−	0.871824i	$-0.662937\pi$
$937$	−29.9872			−0.979640			−0.489820	+	0.871824i	$0.662937\pi$
$938$	−27.9173	+	7.48043i	−0.911534	+	0.244245i
$939$	−19.6531	+	1.51373i	−0.641355	+	0.0493987i
$940$	−12.8652	+	7.42771i	−0.419616	+	0.242265i
$941$	−52.5754	+	14.0875i	−1.71391	+	0.459241i	−0.976378	−	0.216071i	$-0.930676\pi$
$941$	−52.5754	+	14.0875i	−1.71391	+	0.459241i	−0.737532	+	0.675312i	$0.764009\pi$
$942$	−63.6867	−	54.5777i	−2.07502	−	1.77824i
$943$	−2.68654	−	2.68654i	−0.0874857	−	0.0874857i
$944$	−15.1780	+	15.1780i	−0.494001	+	0.494001i
$945$	−7.76625	−	2.34284i	−0.252636	−	0.0762125i
$946$	3.55458	−	2.05224i	0.115569	−	0.0667239i
$947$	−5.99590	−	22.3770i	−0.194841	−	0.727155i	−0.992308	−	0.123793i	$-0.960494\pi$
$947$	−5.99590	−	22.3770i	−0.194841	−	0.727155i	0.797467	−	0.603362i	$-0.206173\pi$
$948$	−48.8471	+	33.4518i	−1.58648	+	1.08646i
$949$	2.96731	+	60.2331i	0.0963230	+	1.95525i
$950$	5.31551	+	3.06891i	0.172458	+	0.0995687i
$951$	19.1412	+	16.4035i	0.620696	+	0.531919i
$952$	19.8720	−	34.4193i	0.644054	−	1.11553i
$953$	12.1812	−	21.0985i	0.394588	−	0.683447i	−0.598460	−	0.801153i	$-0.704221\pi$
$953$	12.1812	−	21.0985i	0.394588	−	0.683447i	0.993049	+	0.117705i	$0.0375538\pi$
$954$	32.9944	−	45.0956i	1.06823	−	1.46002i
$955$	−1.98881	−	7.42234i	−0.0643564	−	0.240181i
$956$	70.3457	−	70.3457i	2.27514	−	2.27514i
$957$	4.21000	+	3.60785i	0.136090	+	0.116625i
$958$	−4.10621	−	7.11217i	−0.132666	−	0.229784i
$959$	0.0114880			0.000370968
$960$	49.6785	+	9.29317i	1.60337	+	0.299936i
$961$	22.8033	−	13.1655i	0.735590	−	0.424693i
$962$	52.6500	−	58.1062i	1.69750	−	1.87342i
$963$	17.8267	+	6.91139i	0.574457	+	0.222717i
$964$	91.6853	+	24.5670i	2.95298	+	0.791250i
$965$	28.7115	+	16.5766i	0.924256	+	0.533619i
$966$	−3.88714	+	2.66201i	−0.125067	+	0.0856488i
$967$	−2.45734	−	9.17092i	−0.0790228	−	0.294917i	0.915093	−	0.403244i	$-0.132117\pi$
$967$	−2.45734	−	9.17092i	−0.0790228	−	0.294917i	−0.994115	+	0.108327i	$0.965451\pi$
$968$	23.9459	−	89.3673i	0.769650	−	2.87237i
$969$	4.71392	−	5.50068i	0.151433	−	0.176707i
$970$	13.2901	−	49.5994i	0.426720	−	1.59254i
$971$	−3.86066	−	2.22895i	−0.123894	−	0.0715304i	0.436772	−	0.899572i	$-0.356122\pi$
$971$	−3.86066	−	2.22895i	−0.123894	−	0.0715304i	−0.560666	+	0.828042i	$0.689455\pi$
$972$	79.8558	+	11.1920i	2.56138	+	0.358985i
$973$	−1.92193	+	7.17273i	−0.0616142	+	0.229947i
$974$	−1.04105	−	1.80316i	−0.0333575	−	0.0577768i
$975$	−9.80406	+	12.6506i	−0.313981	+	0.405142i
$976$	−37.7268	+	65.3448i	−1.20761	+	2.09164i
$977$	16.5129	+	16.5129i	0.528295	+	0.528295i	0.920064	−	0.391769i	$-0.128137\pi$
$977$	16.5129	+	16.5129i	0.528295	+	0.528295i	−0.391769	+	0.920064i	$0.628137\pi$
$978$	−8.86753	−	115.129i	−0.283552	−	3.68143i
$979$			0.409761i			0.0130960i
$980$	−5.71025	−	5.71025i	−0.182407	−	0.182407i
$981$	47.9790	+	5.20481i	1.53185	+	0.166177i
$982$	110.810	−	29.6914i	3.53608	−	0.947489i
$983$	−3.54673	−	0.950342i	−0.113123	−	0.0303112i	0.201813	−	0.979424i	$-0.435317\pi$
$983$	−3.54673	−	0.950342i	−0.113123	−	0.0303112i	−0.314936	+	0.949113i	$0.601983\pi$
$984$	−23.7863	+	49.6555i	−0.758280	+	1.58296i
$985$		−	38.0658i		−	1.21288i
$986$	−84.6883	+	84.6883i	−2.69703	+	2.69703i
$987$	−3.17681	+	0.244685i	−0.101119	+	0.00778842i
$988$	−0.820634	−	16.6580i	−0.0261078	−	0.529960i
$989$		−	4.64902i		−	0.147830i
$990$	−0.452903	+	4.17496i	−0.0143942	+	0.132689i
$991$	4.29464	+	7.43854i	0.136424	+	0.236293i	0.926140	−	0.377179i	$-0.123106\pi$
$991$	4.29464	+	7.43854i	0.136424	+	0.236293i	−0.789717	+	0.613472i	$0.789772\pi$
$992$	35.1089			1.11471
$993$	−14.6491	−	41.5883i	−0.464875	−	1.31976i
$994$	9.96574	+	2.67031i	0.316094	+	0.0846972i
$995$	26.4374	+	7.08387i	0.838121	+	0.224574i
$996$	112.982	+	21.1352i	3.57998	+	0.669694i
$997$	46.2485			1.46471			0.732353	−	0.680925i	$-0.238422\pi$
$997$	46.2485			1.46471			0.732353	+	0.680925i	$0.238422\pi$
$998$	−1.50300	−	2.60327i	−0.0475766	−	0.0824050i
$999$	−1.31571	+	42.1729i	−0.0416271	+	1.33429i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	819.2.fy.a.743.82	yes	336
9.2	odd	6		819.2.ew.a.470.82	yes	336
13.7	odd	12		819.2.ew.a.176.82	✓	336
117.20	even	12	inner	819.2.fy.a.722.82	yes	336

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
819.2.ew.a.176.82	✓	336	13.7	odd	12
819.2.ew.a.470.82	yes	336	9.2	odd	6
819.2.fy.a.722.82	yes	336	117.20	even	12	inner
819.2.fy.a.743.82	yes	336	1.1	even	1	trivial

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 819 = 3^{2} \cdot 7 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	819.fy (of order \(12\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(2.58695 - 0.693172i) q^{2} +(0.748276 - 1.56208i) q^{3} +(4.47979 - 2.58641i) q^{4} +(-1.50795 + 0.404053i) q^{5} +(0.852967 - 4.55970i) q^{6} +(-0.707107 - 0.707107i) q^{7} +(6.00863 - 6.00863i) q^{8} +(-1.88017 - 2.33773i) q^{9} +O(q^{10})\)	\(q+(2.58695 - 0.693172i) q^{2} +(0.748276 - 1.56208i) q^{3} +(4.47979 - 2.58641i) q^{4} +(-1.50795 + 0.404053i) q^{5} +(0.852967 - 4.55970i) q^{6} +(-0.707107 - 0.707107i) q^{7} +(6.00863 - 6.00863i) q^{8} +(-1.88017 - 2.33773i) q^{9} +(-3.62091 + 2.09054i) q^{10} +(0.0866523 + 0.323391i) q^{11} +(-0.688050 - 8.93313i) q^{12} +(2.67187 + 2.42098i) q^{13} +(-2.31940 - 1.33911i) q^{14} +(-0.497198 + 2.65787i) q^{15} +(6.20621 - 10.7495i) q^{16} +(-2.33857 + 4.05053i) q^{17} +(-6.48435 - 4.74432i) q^{18} +(-0.231444 - 0.863760i) q^{19} +(-5.71025 + 5.71025i) q^{20} +(-1.63367 + 0.575444i) q^{21} +(0.448331 + 0.776532i) q^{22} +1.01562 q^{23} +(-4.88983 - 13.8820i) q^{24} +(-2.21948 + 1.28142i) q^{25} +(8.59015 + 4.41089i) q^{26} +(-5.05859 + 1.18770i) q^{27} +(-4.99656 - 1.33882i) q^{28} +(8.28025 + 4.78060i) q^{29} +(0.556135 + 7.22044i) q^{30} +(0.559255 + 2.08717i) q^{31} +(4.20532 - 15.6945i) q^{32} +(0.570001 + 0.106628i) q^{33} +(-3.24207 + 12.0996i) q^{34} +(1.35199 + 0.780571i) q^{35} +(-14.4691 - 5.60965i) q^{36} +(2.10164 - 7.84344i) q^{37} +(-1.19747 - 2.07408i) q^{38} +(5.78104 - 2.36211i) q^{39} +(-6.63289 + 11.4885i) q^{40} +(-2.64521 - 2.64521i) q^{41} +(-3.82734 + 2.62106i) q^{42} -4.57750i q^{43} +(1.22460 + 1.22460i) q^{44} +(3.77976 + 2.76548i) q^{45} +(2.62737 - 0.704002i) q^{46} +(1.77688 + 0.476115i) q^{47} +(-12.1475 - 17.7381i) q^{48} +1.00000i q^{49} +(-4.85345 + 4.85345i) q^{50} +(4.57734 + 6.68394i) q^{51} +(18.2310 + 3.93492i) q^{52} +6.95452i q^{53} +(-12.2631 + 6.57900i) q^{54} +(-0.261334 - 0.452644i) q^{55} -8.49748 q^{56} +(-1.52244 - 0.284798i) q^{57} +(24.7344 + 6.62756i) q^{58} +(-1.67038 - 0.447578i) q^{59} +(4.64700 + 13.1927i) q^{60} -6.07889 q^{61} +(2.89353 + 5.01175i) q^{62} +(-0.323544 + 2.98250i) q^{63} -18.6911i q^{64} +(-5.00724 - 2.57113i) q^{65} +(1.54848 - 0.119267i) q^{66} +(7.63081 - 7.63081i) q^{67} +24.1940i q^{68} +(0.759967 - 1.58648i) q^{69} +(4.03860 + 1.08214i) q^{70} +(-3.72104 + 0.997051i) q^{71} +(-25.3438 - 2.74931i) q^{72} +(11.8270 + 11.8270i) q^{73} -21.7474i q^{74} +(0.340889 + 4.42585i) q^{75} +(-3.27086 - 3.27086i) q^{76} +(0.167399 - 0.289944i) q^{77} +(13.3179 - 10.1179i) q^{78} +(-3.30393 - 5.72257i) q^{79} +(-5.01528 + 18.7173i) q^{80} +(-1.92994 + 8.79064i) q^{81} +(-8.67662 - 5.00945i) q^{82} +(-3.32038 + 12.3918i) q^{83} +(-5.83015 + 6.80320i) q^{84} +(1.88982 - 7.05289i) q^{85} +(-3.17300 - 11.8418i) q^{86} +(13.6636 - 9.35717i) q^{87} +(2.46379 + 1.42247i) q^{88} +(1.18220 + 0.316770i) q^{89} +(11.6950 + 4.53416i) q^{90} +(-0.177408 - 3.60118i) q^{91} +(4.54979 - 2.62682i) q^{92} +(3.67879 + 0.688178i) q^{93} +4.92675 q^{94} +(0.698010 + 1.20899i) q^{95} +(-21.3692 - 18.3128i) q^{96} +(-8.68421 + 8.68421i) q^{97} +(0.693172 + 2.58695i) q^{98} +(0.593079 - 0.810598i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 336 q - 12 q^{6} + 36 q^{8}+O(q^{10}) \) 336 * q - 12 * q^6 + 36 * q^8	\( 336 q - 12 q^{6} + 36 q^{8} - 12 q^{11} + 4 q^{15} + 168 q^{16} - 4 q^{18} - 4 q^{21} + 8 q^{24} - 96 q^{26} + 24 q^{27} - 120 q^{30} - 72 q^{32} + 36 q^{33} + 72 q^{38} + 8 q^{39} - 48 q^{41} - 76 q^{45} + 24 q^{48} - 24 q^{50} - 36 q^{52} + 72 q^{54} + 32 q^{57} + 36 q^{58} - 72 q^{59} + 4 q^{60} + 36 q^{62} - 8 q^{63} - 72 q^{65} - 20 q^{66} - 48 q^{71} - 176 q^{72} - 60 q^{75} - 124 q^{78} - 12 q^{79} - 96 q^{80} - 20 q^{81} - 156 q^{83} - 12 q^{84} - 108 q^{85} - 24 q^{87} + 60 q^{89} - 72 q^{92} + 20 q^{93} + 96 q^{94} + 88 q^{96} - 96 q^{97} + 108 q^{99}+O(q^{100}) \) 336 * q - 12 * q^6 + 36 * q^8 - 12 * q^11 + 4 * q^15 + 168 * q^16 - 4 * q^18 - 4 * q^21 + 8 * q^24 - 96 * q^26 + 24 * q^27 - 120 * q^30 - 72 * q^32 + 36 * q^33 + 72 * q^38 + 8 * q^39 - 48 * q^41 - 76 * q^45 + 24 * q^48 - 24 * q^50 - 36 * q^52 + 72 * q^54 + 32 * q^57 + 36 * q^58 - 72 * q^59 + 4 * q^60 + 36 * q^62 - 8 * q^63 - 72 * q^65 - 20 * q^66 - 48 * q^71 - 176 * q^72 - 60 * q^75 - 124 * q^78 - 12 * q^79 - 96 * q^80 - 20 * q^81 - 156 * q^83 - 12 * q^84 - 108 * q^85 - 24 * q^87 + 60 * q^89 - 72 * q^92 + 20 * q^93 + 96 * q^94 + 88 * q^96 - 96 * q^97 + 108 * q^99

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